Anmelden (DTAQ) DWDS     dlexDB     CLARIN-D

Schröder, Ernst: Vorlesungen über die Algebra der Logik. Bd. 2, Abt. 1. Leipzig, 1891.

Bild:
<< vorherige Seite
nächste Seite >>

§ 37. Produkte und Summen der Grundbeziehungen.
VI0. Produkte der Grundbeziehungen mit den Hülfs-
beziehungen h, h1, k, k1.
h k = h k a,h k1 = h k1 a,h1 k = h1 k a, h1 k1 = h1 k1 a + a1.
a1 h = 0,a1 h1 = a1,a h = h,a h1 = h1 a,
a1 k = 0,a1 k1 = a1,a k = k,a k1 = k1 a,
b h = h k,b h1 = e + d,b1 h = h k1,b1 h1 = h1 k1 a + a + g,
b k = k,b k1 = b + d, b1 k = 0,b1 k1 = b1
c h = h,c h1 = g + d,c1 h = 0,c1 h1 = c1,
c k = h k,c k1 = f + d,c1 k = h1 k,c1 k1 = h1 k1 a + a + b,
d h = h k,d h1 = d,d1 h = h k1,d1 h1 = c1 + g,
d k = h k,d k1 = d,d1 k = h1 k,d1 k1 = b1 + b,
e h = 0,e h1 = e,e1 h = h,e1 h1 = h1 k1 a + a + g + d,
e k = h1 k,e k1 = b,e1 k = h k,e1 k1 = b1 + d,
f h = h k1,f h1 = g,f1 h = h k,f1 h1 = c1 + d,
f k = 0,f k1 = f,f1 k = k,f1 k1 = h1 k1 a + a + b + d,
g h = 0,g h1 = g,g1 h = h,g1 h1 = h1 a + b + g + d,
g k = 0,g k1 = g,g1 k = k,g1 k1 = k1 a + b + g + d.
VII0. Summen der Grundbeziehungen mit den h, h1, k, k1.
h + k = (h + k) a,h + k1 = e1 + b,h1 + k = f1 + g,h1 + k1 = d1 + d,
a1 + h = h + a1,a1 + h1 = h1,a + h = a,a + h1 = i,
a1 + k = k + a1,a1 + k1 = k1,a + k = a,a + k1 = i,
b + h = h + b,b + h1 = f1 + g,b1 + h = h + b1,b1 + h1 = d1 + d,
b + k = b,b + k1 = i,b1 + k = a + a + g,b1 + k1 = k1,
c + h = c,c + h1 = i,c1 + h = a + a + b,c1 + h1 = h1,
c + k = k + c,c + k1 = c1 + b,c1 + k = k + c1,c1 + k1 = d1 + d,
d + h = h + d,d + h1 = f1 + g,d1 + h = a + a + b + g,d1 + h1 = d1 + d,
d + k = k + d,d + k1 = e1 + b,d1 + k = a + a + b + g,d1 + k1 = d1 + d,
e + h = (h + k) + b,e + h1 = h1,e1 + h = e1,e1 + h1 = i,
e + k = k + b,e + k1 = d1 + d,e1 + k = a + a + g + d,e1 + k1 = e1 + b,
f + h = h + g,f + h1 = d1 + d,f1 + h = a + a + b + d,f1 + h1 = f1 + g,
f + k = (h + k) + g,f + k1 = k1,f1 + k = f1,f1 + k1 = i,
g + h = h + a,g + h1 = h1,g1 + h = g1,g1 + h1 = i,
g + k = k + a,g + k1 = k1,g1 + k = g1,g1 + k1 = i.

§ 37. Produkte und Summen der Grundbeziehungen.
VI0. Produkte der Grundbeziehungen mit den Hülfs-
beziehungen h, h1, k, k1.
h k = h k a,h k1 = h k1 a,h1 k = h1 k a, h1 k1 = h1 k1 a + a1.
a1 h = 0,a1 h1 = a1,a h = h,a h1 = h1 a,
a1 k = 0,a1 k1 = a1,a k = k,a k1 = k1 a,
b h = h k,b h1 = e + δ,b1 h = h k1,b1 h1 = h1 k1 a + α + γ,
b k = k,b k1 = β + δ, b1 k = 0,b1 k1 = b1
c h = h,c h1 = γ + δ,c1 h = 0,c1 h1 = c1,
c k = h k,c k1 = f + δ,c1 k = h1 k,c1 k1 = h1 k1 a + α + β,
d h = h k,d h1 = δ,d1 h = h k1,d1 h1 = c1 + γ,
d k = h k,d k1 = δ,d1 k = h1 k,d1 k1 = b1 + β,
e h = 0,e h1 = e,e1 h = h,e1 h1 = h1 k1 a + α + γ + δ,
e k = h1 k,e k1 = β,e1 k = h k,e1 k1 = b1 + δ,
f h = h k1,f h1 = γ,f1 h = h k,f1 h1 = c1 + δ,
f k = 0,f k1 = f,f1 k = k,f1 k1 = h1 k1 a + α + β + δ,
g h = 0,g h1 = g,g1 h = h,g1 h1 = h1 a + β + γ + δ,
g k = 0,g k1 = g,g1 k = k,g1 k1 = k1 a + β + γ + δ.
VII0. Summen der Grundbeziehungen mit den h, h1, k, k1.
h + k = (h + k) a,h + k1 = e1 + β,h1 + k = f1 + γ,h1 + k1 = d1 + δ,
a1 + h = h + a1,a1 + h1 = h1,a + h = a,a + h1 = i,
a1 + k = k + a1,a1 + k1 = k1,a + k = a,a + k1 = i,
b + h = h + b,b + h1 = f1 + γ,b1 + h = h + b1,b1 + h1 = d1 + δ,
b + k = b,b + k1 = i,b1 + k = a + α + γ,b1 + k1 = k1,
c + h = c,c + h1 = i,c1 + h = a + α + β,c1 + h1 = h1,
c + k = k + c,c + k1 = c1 + β,c1 + k = k + c1,c1 + k1 = d1 + δ,
d + h = h + δ,d + h1 = f1 + γ,d1 + h = a + α + β + γ,d1 + h1 = d1 + δ,
d + k = k + δ,d + k1 = e1 + β,d1 + k = a + α + β + γ,d1 + k1 = d1 + δ,
e + h = (h + k) + β,e + h1 = h1,e1 + h = e1,e1 + h1 = i,
e + k = k + β,e + k1 = d1 + δ,e1 + k = a + α + γ + δ,e1 + k1 = e1 + β,
f + h = h + γ,f + h1 = d1 + δ,f1 + h = a + α + β + δ,f1 + h1 = f1 + γ,
f + k = (h + k) + γ,f + k1 = k1,f1 + k = f1,f1 + k1 = i,
g + h = h + α,g + h1 = h1,g1 + h = g1,g1 + h1 = i,
g + k = k + α,g + k1 = k1,g1 + k = g1,g1 + k1 = i.

<TEI>
  <text>
    <body>
      <div n="1">
        <div n="2">
          <div n="3">
            <p>
              <pb facs="#f0149" n="125"/>
              <fw place="top" type="header">§ 37. Produkte und Summen der Grundbeziehungen.</fw><lb/> <hi rendition="#c">VI<hi rendition="#sup">0</hi>. <hi rendition="#g">Produkte der Grundbeziehungen mit den Hülfs-<lb/>
beziehungen</hi> <hi rendition="#i">h</hi>, <hi rendition="#i">h</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">k</hi>, <hi rendition="#i">k</hi><hi rendition="#sub">1</hi>.</hi><lb/>
              <table>
                <row>
                  <cell><hi rendition="#i">h k</hi> = <hi rendition="#i">h k a</hi>,</cell>
                  <cell><hi rendition="#i">h k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi>,</cell>
                  <cell><hi rendition="#i">h</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k a</hi>,</cell>
                  <cell><hi rendition="#i">h</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi> + <hi rendition="#i">a</hi><hi rendition="#sub">1</hi>.</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi> = 0,</cell>
                  <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi><hi rendition="#sub">1</hi>,</cell>
                  <cell><hi rendition="#i">a h</hi> = <hi rendition="#i">h</hi>,</cell>
                  <cell><hi rendition="#i">a h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi>,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi> = 0,</cell>
                  <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi><hi rendition="#sub">1</hi>,</cell>
                  <cell><hi rendition="#i">a k</hi> = <hi rendition="#i">k</hi>,</cell>
                  <cell><hi rendition="#i">a k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi>,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">b h</hi> = <hi rendition="#i">h k</hi>,</cell>
                  <cell><hi rendition="#i">b h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">e</hi> + <hi rendition="#i">&#x03B4;</hi>,</cell>
                  <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi> = <hi rendition="#i">h k</hi><hi rendition="#sub">1</hi>,</cell>
                  <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi> + <hi rendition="#i">&#x03B1;</hi> + <hi rendition="#i">&#x03B3;</hi>,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">b k</hi> = <hi rendition="#i">k</hi>,</cell>
                  <cell><hi rendition="#i">b k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">&#x03B2;</hi> + <hi rendition="#i">&#x03B4;</hi>,</cell>
                  <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi> = 0,</cell>
                  <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">b</hi><hi rendition="#sub">1</hi></cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">c h</hi> = <hi rendition="#i">h</hi>,</cell>
                  <cell><hi rendition="#i">c h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">&#x03B3;</hi> + <hi rendition="#i">&#x03B4;</hi>,</cell>
                  <cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi> = 0,</cell>
                  <cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">c</hi><hi rendition="#sub">1</hi>,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">c k</hi> = <hi rendition="#i">h k</hi>,</cell>
                  <cell><hi rendition="#i">c k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">f</hi> + <hi rendition="#i">&#x03B4;</hi>,</cell>
                  <cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi>,</cell>
                  <cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi> + <hi rendition="#i">&#x03B1;</hi> + <hi rendition="#i">&#x03B2;</hi>,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">d h</hi> = <hi rendition="#i">h k</hi>,</cell>
                  <cell><hi rendition="#i">d h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">&#x03B4;</hi>,</cell>
                  <cell><hi rendition="#i">d</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi> = <hi rendition="#i">h k</hi><hi rendition="#sub">1</hi>,</cell>
                  <cell><hi rendition="#i">d</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">c</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">&#x03B3;</hi>,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">d k</hi> = <hi rendition="#i">h k</hi>,</cell>
                  <cell><hi rendition="#i">d k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">&#x03B4;</hi>,</cell>
                  <cell><hi rendition="#i">d</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi>,</cell>
                  <cell><hi rendition="#i">d</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">b</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">&#x03B2;</hi>,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">e h</hi> = 0,</cell>
                  <cell><hi rendition="#i">e h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">e</hi>,</cell>
                  <cell><hi rendition="#i">e</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi> = <hi rendition="#i">h</hi>,</cell>
                  <cell><hi rendition="#i">e</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi> + <hi rendition="#i">&#x03B1;</hi> + <hi rendition="#i">&#x03B3;</hi> + <hi rendition="#i">&#x03B4;</hi>,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">e k</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi>,</cell>
                  <cell><hi rendition="#i">e k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">&#x03B2;</hi>,</cell>
                  <cell><hi rendition="#i">e</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi> = <hi rendition="#i">h k</hi>,</cell>
                  <cell><hi rendition="#i">e</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">b</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">&#x03B4;</hi>,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">f h</hi> = <hi rendition="#i">h k</hi><hi rendition="#sub">1</hi>,</cell>
                  <cell><hi rendition="#i">f h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">&#x03B3;</hi>,</cell>
                  <cell><hi rendition="#i">f</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi> = <hi rendition="#i">h k</hi>,</cell>
                  <cell><hi rendition="#i">f</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">c</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">&#x03B4;</hi>,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">f k</hi> = 0,</cell>
                  <cell><hi rendition="#i">f k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">f</hi>,</cell>
                  <cell><hi rendition="#i">f</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi> = <hi rendition="#i">k</hi>,</cell>
                  <cell><hi rendition="#i">f</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi> + <hi rendition="#i">&#x03B1;</hi> + <hi rendition="#i">&#x03B2;</hi> + <hi rendition="#i">&#x03B4;</hi>,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">g h</hi> = 0,</cell>
                  <cell><hi rendition="#i">g h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">g</hi>,</cell>
                  <cell><hi rendition="#i">g</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi> = <hi rendition="#i">h</hi>,</cell>
                  <cell><hi rendition="#i">g</hi><hi rendition="#sub">1</hi><hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi> + <hi rendition="#i">&#x03B2;</hi> + <hi rendition="#i">&#x03B3;</hi> + <hi rendition="#i">&#x03B4;</hi>,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">g k</hi> = 0,</cell>
                  <cell><hi rendition="#i">g k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">g</hi>,</cell>
                  <cell><hi rendition="#i">g</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi> = <hi rendition="#i">k</hi>,</cell>
                  <cell><hi rendition="#i">g</hi><hi rendition="#sub">1</hi><hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi> + <hi rendition="#i">&#x03B2;</hi> + <hi rendition="#i">&#x03B3;</hi> + <hi rendition="#i">&#x03B4;</hi>.</cell>
                </row><lb/>
              </table> <hi rendition="#c">VII<hi rendition="#sup">0</hi>. <hi rendition="#g">Summen der Grundbeziehungen mit den</hi> <hi rendition="#i">h</hi>, <hi rendition="#i">h</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">k</hi>, <hi rendition="#i">k</hi><hi rendition="#sub">1</hi>.</hi><lb/>
              <table>
                <row>
                  <cell><hi rendition="#i">h</hi> + <hi rendition="#i">k</hi> = (<hi rendition="#i">h</hi> + <hi rendition="#i">k</hi>) <hi rendition="#i">a</hi>,</cell>
                  <cell><hi rendition="#i">h</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">e</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">&#x03B2;</hi>,</cell>
                  <cell><hi rendition="#i">h</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">f</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">&#x03B3;</hi>,</cell>
                  <cell><hi rendition="#i">h</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">d</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">&#x03B4;</hi>,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">h</hi> + <hi rendition="#i">a</hi><hi rendition="#sub">1</hi>,</cell>
                  <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi>,</cell>
                  <cell><hi rendition="#i">a</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">a</hi>,</cell>
                  <cell><hi rendition="#i">a</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = i,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">k</hi> + <hi rendition="#i">a</hi><hi rendition="#sub">1</hi>,</cell>
                  <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">k</hi><hi rendition="#sub">1</hi>,</cell>
                  <cell><hi rendition="#i">a</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">a</hi>,</cell>
                  <cell><hi rendition="#i">a</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = i,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">b</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">h</hi> + <hi rendition="#i">b</hi>,</cell>
                  <cell><hi rendition="#i">b</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">f</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">&#x03B3;</hi>,</cell>
                  <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">h</hi> + <hi rendition="#i">b</hi><hi rendition="#sub">1</hi>,</cell>
                  <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">d</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">&#x03B4;</hi>,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">b</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">b</hi>,</cell>
                  <cell><hi rendition="#i">b</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = i,</cell>
                  <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">&#x03B1;</hi> + <hi rendition="#i">&#x03B3;</hi>,</cell>
                  <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">k</hi><hi rendition="#sub">1</hi>,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">c</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">c</hi>,</cell>
                  <cell><hi rendition="#i">c</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = i,</cell>
                  <cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">&#x03B1;</hi> + <hi rendition="#i">&#x03B2;</hi>,</cell>
                  <cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi>,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">c</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">k</hi> + <hi rendition="#i">c</hi>,</cell>
                  <cell><hi rendition="#i">c</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">c</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">&#x03B2;</hi>,</cell>
                  <cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">k</hi> + <hi rendition="#i">c</hi><hi rendition="#sub">1</hi>,</cell>
                  <cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">d</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">&#x03B4;</hi>,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">d</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">h</hi> + <hi rendition="#i">&#x03B4;</hi>,</cell>
                  <cell><hi rendition="#i">d</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">f</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">&#x03B3;</hi>,</cell>
                  <cell><hi rendition="#i">d</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">&#x03B1;</hi> + <hi rendition="#i">&#x03B2;</hi> + <hi rendition="#i">&#x03B3;</hi>,</cell>
                  <cell><hi rendition="#i">d</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">d</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">&#x03B4;</hi>,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">d</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">k</hi> + <hi rendition="#i">&#x03B4;</hi>,</cell>
                  <cell><hi rendition="#i">d</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">e</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">&#x03B2;</hi>,</cell>
                  <cell><hi rendition="#i">d</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">&#x03B1;</hi> + <hi rendition="#i">&#x03B2;</hi> + <hi rendition="#i">&#x03B3;</hi>,</cell>
                  <cell><hi rendition="#i">d</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">d</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">&#x03B4;</hi>,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">e</hi> + <hi rendition="#i">h</hi> = (<hi rendition="#i">h</hi> + <hi rendition="#i">k</hi>) + <hi rendition="#i">&#x03B2;</hi>,</cell>
                  <cell><hi rendition="#i">e</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi>,</cell>
                  <cell><hi rendition="#i">e</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">e</hi><hi rendition="#sub">1</hi>,</cell>
                  <cell><hi rendition="#i">e</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = i,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">e</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">k</hi> + <hi rendition="#i">&#x03B2;</hi>,</cell>
                  <cell><hi rendition="#i">e</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">d</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">&#x03B4;</hi>,</cell>
                  <cell><hi rendition="#i">e</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">&#x03B1;</hi> + <hi rendition="#i">&#x03B3;</hi> + <hi rendition="#i">&#x03B4;</hi>,</cell>
                  <cell><hi rendition="#i">e</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">e</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">&#x03B2;</hi>,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">f</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">h</hi> + <hi rendition="#i">&#x03B3;</hi>,</cell>
                  <cell><hi rendition="#i">f</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">d</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">&#x03B4;</hi>,</cell>
                  <cell><hi rendition="#i">f</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">&#x03B1;</hi> + <hi rendition="#i">&#x03B2;</hi> + <hi rendition="#i">&#x03B4;</hi>,</cell>
                  <cell><hi rendition="#i">f</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">f</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">&#x03B3;</hi>,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">f</hi> + <hi rendition="#i">k</hi> = (<hi rendition="#i">h</hi> + <hi rendition="#i">k</hi>) + <hi rendition="#i">&#x03B3;</hi>,</cell>
                  <cell><hi rendition="#i">f</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">k</hi><hi rendition="#sub">1</hi>,</cell>
                  <cell><hi rendition="#i">f</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">f</hi><hi rendition="#sub">1</hi>,</cell>
                  <cell><hi rendition="#i">f</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = i,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">g</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">h</hi> + <hi rendition="#i">&#x03B1;</hi>,</cell>
                  <cell><hi rendition="#i">g</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi>,</cell>
                  <cell><hi rendition="#i">g</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi> = <hi rendition="#i">g</hi><hi rendition="#sub">1</hi>,</cell>
                  <cell><hi rendition="#i">g</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = i,</cell>
                </row><lb/>
                <row>
                  <cell><hi rendition="#i">g</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">k</hi> + <hi rendition="#i">&#x03B1;</hi>,</cell>
                  <cell><hi rendition="#i">g</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">k</hi><hi rendition="#sub">1</hi>,</cell>
                  <cell><hi rendition="#i">g</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi> = <hi rendition="#i">g</hi><hi rendition="#sub">1</hi>,</cell>
                  <cell><hi rendition="#i">g</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = i.</cell>
                </row><lb/>
              </table>
            </p>
          </div>
        </div>
      </div>
    </body>
  </text>
</TEI>
[125/0149] § 37. Produkte und Summen der Grundbeziehungen. VI0. Produkte der Grundbeziehungen mit den Hülfs- beziehungen h, h1, k, k1. h k = h k a, h k1 = h k1 a, h1 k = h1 k a, h1 k1 = h1 k1 a + a1. a1 h = 0, a1 h1 = a1, a h = h, a h1 = h1 a, a1 k = 0, a1 k1 = a1, a k = k, a k1 = k1 a, b h = h k, b h1 = e + δ, b1 h = h k1, b1 h1 = h1 k1 a + α + γ, b k = k, b k1 = β + δ, b1 k = 0, b1 k1 = b1 c h = h, c h1 = γ + δ, c1 h = 0, c1 h1 = c1, c k = h k, c k1 = f + δ, c1 k = h1 k, c1 k1 = h1 k1 a + α + β, d h = h k, d h1 = δ, d1 h = h k1, d1 h1 = c1 + γ, d k = h k, d k1 = δ, d1 k = h1 k, d1 k1 = b1 + β, e h = 0, e h1 = e, e1 h = h, e1 h1 = h1 k1 a + α + γ + δ, e k = h1 k, e k1 = β, e1 k = h k, e1 k1 = b1 + δ, f h = h k1, f h1 = γ, f1 h = h k, f1 h1 = c1 + δ, f k = 0, f k1 = f, f1 k = k, f1 k1 = h1 k1 a + α + β + δ, g h = 0, g h1 = g, g1 h = h, g1 h1 = h1 a + β + γ + δ, g k = 0, g k1 = g, g1 k = k, g1 k1 = k1 a + β + γ + δ. VII0. Summen der Grundbeziehungen mit den h, h1, k, k1. h + k = (h + k) a, h + k1 = e1 + β, h1 + k = f1 + γ, h1 + k1 = d1 + δ, a1 + h = h + a1, a1 + h1 = h1, a + h = a, a + h1 = i, a1 + k = k + a1, a1 + k1 = k1, a + k = a, a + k1 = i, b + h = h + b, b + h1 = f1 + γ, b1 + h = h + b1, b1 + h1 = d1 + δ, b + k = b, b + k1 = i, b1 + k = a + α + γ, b1 + k1 = k1, c + h = c, c + h1 = i, c1 + h = a + α + β, c1 + h1 = h1, c + k = k + c, c + k1 = c1 + β, c1 + k = k + c1, c1 + k1 = d1 + δ, d + h = h + δ, d + h1 = f1 + γ, d1 + h = a + α + β + γ, d1 + h1 = d1 + δ, d + k = k + δ, d + k1 = e1 + β, d1 + k = a + α + β + γ, d1 + k1 = d1 + δ, e + h = (h + k) + β, e + h1 = h1, e1 + h = e1, e1 + h1 = i, e + k = k + β, e + k1 = d1 + δ, e1 + k = a + α + γ + δ, e1 + k1 = e1 + β, f + h = h + γ, f + h1 = d1 + δ, f1 + h = a + α + β + δ, f1 + h1 = f1 + γ, f + k = (h + k) + γ, f + k1 = k1, f1 + k = f1, f1 + k1 = i, g + h = h + α, g + h1 = h1, g1 + h = g1, g1 + h1 = i, g + k = k + α, g + k1 = k1, g1 + k = g1, g1 + k1 = i.

Suche im Werk

Hilfe

Informationen zum Werk

Download dieses Werks

XML (TEI P5) · HTML · Text
TCF (text annotation layer)
TCF (tokenisiert, serialisiert, lemmatisiert, normalisiert)
XML (TEI P5 inkl. att.linguistic)

Metadaten zum Werk

TEI-Header · CMDI · Dublin Core

Ansichten dieser Seite

Voyant Tools ?

Language Resource Switchboard?

Feedback

Sie haben einen Fehler gefunden? Dann können Sie diesen über unsere Qualitätssicherungsplattform DTAQ melden.

Kommentar zur DTA-Ausgabe

Dieses Werk wurde gemäß den DTA-Transkriptionsrichtlinien im Double-Keying-Verfahren von Nicht-Muttersprachlern erfasst und in XML/TEI P5 nach DTA-Basisformat kodiert.




Ansicht auf Standard zurückstellen

URL zu diesem Werk: https://www.deutschestextarchiv.de/schroeder_logik0201_1891
URL zu dieser Seite: https://www.deutschestextarchiv.de/schroeder_logik0201_1891/149
Zitationshilfe: Schröder, Ernst: Vorlesungen über die Algebra der Logik. Bd. 2, Abt. 1. Leipzig, 1891, S. 125. In: Deutsches Textarchiv <https://www.deutschestextarchiv.de/schroeder_logik0201_1891/149>, abgerufen am 25.04.2024.