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

Bild:
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Dreiundzwanzigste Vorlesung.

81'. e1A, B1 = f1A1, B = (A1 + B1 = 1) + (A1 B1 0)

91'. f1A, B1 = e1A1, B = (A + B = 1) + (A B 0)

101'. f1 = f1A, B = e1A1, B1 = (A + B1 = 1) + (A B1 0).

Beziehungen, welche zugleich Grund-, Elementar- und
primitive Beziehungen sind (zusammen mit ihren Negationen die
8 Beziehungen De Morgan's).

11'. a = aA, B = cA, B1 = bA1, B = lA1, B1 = (A1 + B1 = 1)

12'. c = cA, B = aA, B1 = bA1, B1 = lA1, B = (A1 + B = 1)

13'. b = bA, B = aA1, B = cA1, B1 = lA, B1 = (A + B1 = 1)

14'. l = lA, B = aA1, B1 = cA1, B = bA, B1 = (A + B = 1)

Negationen derselben.

111'. a1 = a1A, B = c1A, B1 = b1A1, B = l1A1, B1 = (A B 0)

121'. c1 = c1A, B = a1A, B1 = b1A1, B1 = l1A1, B = (A B1 0)

131'. b1 = b1A, B = a1A1, B = c1A1, B1 = l1A, B1 = (A1 B 0)

141'. l1 = l1A, B = a1A1, B1 = c1A1, B = b1A, B1 = (A1 B1 0)

(Nicht-primitive, resp.) Die übrigen Beziehungen, welche zu-
gleich Grund- und Elementarbeziehungen sind.

15'. g = gA, B = (A B 0) (A B1 0) (A1 B 0) = aA, B = a

16'. gA, B1 = (A B 0) (A B1 0) (A1 B1 0) = aA, B1

17'. gA1, B = (A B 0) (A1 B 0) (A1 B1 0) = aA1, B

18'. gA1, B1 = (A B1 0) (A1 B 0) (A1 B1 0) = aA1, B1

Verneinungen derselben.

151'. g1 = g1A, B = (A1 + B1 = 1) + (A1 + B = 1) + (A + B1 = 1) = a1A, B = a1

161'. g1A, B1 = (A1 + B1 = 1) + (A1 + B = 1) + (A + B = 1) = a1A, B1

171'. g1A1, B = (A1 + B1 = 1) + (A + B1 = 1) + (A + B = 1) = a1A1, B

181'. g1A1, B1 = (A1 + B = 1) + (A + B1 = 1) + (A + B = 1) = a1A1, B1

Die Beziehungen, welche nur Elementarbeziehungen sind.

19'. b = bA, B = (A + B1 = 1) (A B 0) (A B1 0)

20'. bA, B1 = (A + B = 1) (A B 0) (A B1 0)

Dreiundzwanzigste Vorlesung.

81’. e1A, B1 = f1A1, B = (A1 + B1 = 1) + (A1 B1 ≠ 0)

91’. f1A, B1 = e1A1, B = (A + B = 1) + (A B ≠ 0)

101’. f1 = f1A, B = e1A1, B1 = (A + B1 = 1) + (A B1 ≠ 0).

Beziehungen, welche zugleich Grund-, Elementar- und
primitive Beziehungen sind (zusammen mit ihren Negationen die
8 Beziehungen De Morgan’s).

11’. a = aA, B = cA, B1 = bA1, B = lA1, B1 = (A1 + B1 = 1)

12’. c = cA, B = aA, B1 = bA1, B1 = lA1, B = (A1 + B = 1)

13’. b = bA, B = aA1, B = cA1, B1 = lA, B1 = (A + B1 = 1)

14’. l = lA, B = aA1, B1 = cA1, B = bA, B1 = (A + B = 1)

Negationen derselben.

111’. a1 = a1A, B = c1A, B1 = b1A1, B = l1A1, B1 = (A B ≠ 0)

121’. c1 = c1A, B = a1A, B1 = b1A1, B1 = l1A1, B = (A B1 ≠ 0)

131’. b1 = b1A, B = a1A1, B = c1A1, B1 = l1A, B1 = (A1 B ≠ 0)

141’. l1 = l1A, B = a1A1, B1 = c1A1, B = b1A, B1 = (A1 B1 ≠ 0)

(Nicht-primitive, resp.) Die übrigen Beziehungen, welche zu-
gleich Grund- und Elementarbeziehungen sind.

15’. g = gA, B = (A B ≠ 0) (A B1 ≠ 0) (A1 B ≠ 0) = αA, B = α

16’. gA, B1 = (A B ≠ 0) (A B1 ≠ 0) (A1 B1 ≠ 0) = αA, B1

17’. gA1, B = (A B ≠ 0) (A1 B ≠ 0) (A1 B1 ≠ 0) = αA1, B

18’. gA1, B1 = (A B1 ≠ 0) (A1 B ≠ 0) (A1 B1 ≠ 0) = αA1, B1

Verneinungen derselben.

151’. g1 = g1A, B = (A1 + B1 = 1) + (A1 + B = 1) + (A + B1 = 1) = α1A, B = α1

161’. g1A, B1 = (A1 + B1 = 1) + (A1 + B = 1) + (A + B = 1) = α1A, B1

171’. g1A1, B = (A1 + B1 = 1) + (A + B1 = 1) + (A + B = 1) = α1A1, B

181’. g1A1, B1 = (A1 + B = 1) + (A + B1 = 1) + (A + B = 1) = α1A1, B1

Die Beziehungen, welche nur Elementarbeziehungen sind.

19’. β = βA, B = (A + B1 = 1) (A B ≠ 0) (A B1 ≠ 0)

20’. βA, B1 = (A + B = 1) (A B ≠ 0) (A B1 ≠ 0)

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            <pb facs="#f0376" n="352"/>
            <fw place="top" type="header">Dreiundzwanzigste Vorlesung.</fw><lb/>
            <p>8<hi rendition="#sub">1</hi>&#x2019;. <hi rendition="#et"><hi rendition="#i">e</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi> = <hi rendition="#i">f</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi></hi> = (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">B</hi><hi rendition="#sub">1</hi> = 1) + (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">B</hi><hi rendition="#sub">1</hi> &#x2260; 0)</hi></p><lb/>
            <p>9<hi rendition="#sub">1</hi>&#x2019;. <hi rendition="#et"><hi rendition="#i">f</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi> = <hi rendition="#i">e</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi></hi> = (<hi rendition="#i">A</hi> + <hi rendition="#i">B</hi> = 1) + (<hi rendition="#i">A B</hi> &#x2260; 0)</hi></p><lb/>
            <p>10<hi rendition="#sub">1</hi>&#x2019;. <hi rendition="#et"><hi rendition="#i">f</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">f</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi></hi> = <hi rendition="#i">e</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi> = (<hi rendition="#i">A</hi> + <hi rendition="#i">B</hi><hi rendition="#sub">1</hi> = 1) + (<hi rendition="#i">A B</hi><hi rendition="#sub">1</hi> &#x2260; 0).</hi></p><lb/>
            <p> <hi rendition="#c"><hi rendition="#g">Beziehungen</hi>, <hi rendition="#g">welche zugleich Grund-</hi>, <hi rendition="#g">Elementar- und<lb/>
primitive Beziehungen sind</hi> (zusammen mit ihren Negationen die<lb/>
8 Beziehungen <hi rendition="#g">De Morgan&#x2019;</hi>s).</hi> </p><lb/>
            <p>11&#x2019;. <hi rendition="#et"><hi rendition="#i">a</hi> = <hi rendition="#i">a</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi></hi> = <hi rendition="#i">c</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi> = <hi rendition="#i">b</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi></hi> = <hi rendition="#i">l</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi> = (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">B</hi><hi rendition="#sub">1</hi> = 1)</hi></p><lb/>
            <p>12&#x2019;. <hi rendition="#et"><hi rendition="#i">c</hi> = <hi rendition="#i">c</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi></hi> = <hi rendition="#i">a</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi> = <hi rendition="#i">b</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi> = <hi rendition="#i">l</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi></hi> = (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">B</hi> = 1)</hi></p><lb/>
            <p>13&#x2019;. <hi rendition="#et"><hi rendition="#i">b</hi> = <hi rendition="#i">b</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi></hi> = <hi rendition="#i">a</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi></hi> = <hi rendition="#i">c</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi> = <hi rendition="#i">l</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi> = (<hi rendition="#i">A</hi> + <hi rendition="#i">B</hi><hi rendition="#sub">1</hi> = 1)</hi></p><lb/>
            <p>14&#x2019;. <hi rendition="#et"><hi rendition="#i">l</hi> = <hi rendition="#i">l</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi></hi> = <hi rendition="#i">a</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi> = <hi rendition="#i">c</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi></hi> = <hi rendition="#i">b</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi> = (<hi rendition="#i">A</hi> + <hi rendition="#i">B</hi> = 1)</hi></p><lb/>
            <p> <hi rendition="#c"><hi rendition="#g">Negationen derselben</hi>.</hi> </p><lb/>
            <p>11<hi rendition="#sub">1</hi>&#x2019;. <hi rendition="#et"><hi rendition="#i">a</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi></hi> = <hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi> = <hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi></hi> = <hi rendition="#i">l</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi> = (<hi rendition="#i">A B</hi> &#x2260; 0)</hi></p><lb/>
            <p>12<hi rendition="#sub">1</hi>&#x2019;. <hi rendition="#et"><hi rendition="#i">c</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi></hi> = <hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi> = <hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi> = <hi rendition="#i">l</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi></hi> = (<hi rendition="#i">A B</hi><hi rendition="#sub">1</hi> &#x2260; 0)</hi></p><lb/>
            <p>13<hi rendition="#sub">1</hi>&#x2019;. <hi rendition="#et"><hi rendition="#i">b</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi></hi> = <hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi></hi> = <hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi> = <hi rendition="#i">l</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi> = (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">B</hi> &#x2260; 0)</hi></p><lb/>
            <p>14<hi rendition="#sub">1</hi>&#x2019;. <hi rendition="#et"><hi rendition="#i">l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">l</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi></hi> = <hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi> = <hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi></hi> = <hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi> = (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">B</hi><hi rendition="#sub">1</hi> &#x2260; 0)</hi></p><lb/>
            <p> <hi rendition="#c">(Nicht-primitive, resp.) <hi rendition="#g">Die übrigen Beziehungen</hi>, <hi rendition="#g">welche zu-<lb/>
gleich Grund- und Elementarbeziehungen sind</hi>.</hi> </p><lb/>
            <p>15&#x2019;. <hi rendition="#et"><hi rendition="#i">g</hi> = <hi rendition="#i">g</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi></hi> = (<hi rendition="#i">A B</hi> &#x2260; 0) (<hi rendition="#i">A B</hi><hi rendition="#sub">1</hi> &#x2260; 0) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">B</hi> &#x2260; 0) = <hi rendition="#i">&#x03B1;</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi></hi> = <hi rendition="#i">&#x03B1;</hi></hi></p><lb/>
            <p>16&#x2019;. <hi rendition="#et"><hi rendition="#i">g</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi> = (<hi rendition="#i">A B</hi> &#x2260; 0) (<hi rendition="#i">A B</hi><hi rendition="#sub">1</hi> &#x2260; 0) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">B</hi><hi rendition="#sub">1</hi> &#x2260; 0) = <hi rendition="#i">&#x03B1;</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi></hi></p><lb/>
            <p>17&#x2019;. <hi rendition="#et"><hi rendition="#i">g</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi></hi> = (<hi rendition="#i">A B</hi> &#x2260; 0) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">B</hi> &#x2260; 0) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">B</hi><hi rendition="#sub">1</hi> &#x2260; 0) = <hi rendition="#i">&#x03B1;</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi></hi></hi></p><lb/>
            <p>18&#x2019;. <hi rendition="#et"><hi rendition="#i">g</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi> = (<hi rendition="#i">A B</hi><hi rendition="#sub">1</hi> &#x2260; 0) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">B</hi> &#x2260; 0) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">B</hi><hi rendition="#sub">1</hi> &#x2260; 0) = <hi rendition="#i">&#x03B1;</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi></hi></p><lb/>
            <p> <hi rendition="#c"><hi rendition="#g">Verneinungen derselben</hi>.</hi> </p><lb/>
            <p>15<hi rendition="#sub">1</hi>&#x2019;. <hi rendition="#et"><hi rendition="#i">g</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">g</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi></hi> = (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">B</hi><hi rendition="#sub">1</hi> = 1) + (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">B</hi> = 1) + (<hi rendition="#i">A</hi> + <hi rendition="#i">B</hi><hi rendition="#sub">1</hi> = 1) = <hi rendition="#i">&#x03B1;</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi></hi> = <hi rendition="#i">&#x03B1;</hi><hi rendition="#sub">1</hi></hi></p><lb/>
            <p>16<hi rendition="#sub">1</hi>&#x2019;. <hi rendition="#et"><hi rendition="#i">g</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi> = (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">B</hi><hi rendition="#sub">1</hi> = 1) + (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">B</hi> = 1) + (<hi rendition="#i">A</hi> + <hi rendition="#i">B</hi> = 1) = <hi rendition="#i">&#x03B1;</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi></hi></p><lb/>
            <p>17<hi rendition="#sub">1</hi>&#x2019;. <hi rendition="#et"><hi rendition="#i">g</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi></hi> = (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">B</hi><hi rendition="#sub">1</hi> = 1) + (<hi rendition="#i">A</hi> + <hi rendition="#i">B</hi><hi rendition="#sub">1</hi> = 1) + (<hi rendition="#i">A</hi> + <hi rendition="#i">B</hi> = 1) = <hi rendition="#i">&#x03B1;</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi></hi></hi></p><lb/>
            <p>18<hi rendition="#sub">1</hi>&#x2019;. <hi rendition="#et"><hi rendition="#i">g</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi> = (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">B</hi> = 1) + (<hi rendition="#i">A</hi> + <hi rendition="#i">B</hi><hi rendition="#sub">1</hi> = 1) + (<hi rendition="#i">A</hi> + <hi rendition="#i">B</hi> = 1) = <hi rendition="#i">&#x03B1;</hi><hi rendition="#sub">1</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi></hi></p><lb/>
            <p> <hi rendition="#c"><hi rendition="#g">Die Beziehungen</hi>, <hi rendition="#g">welche nur Elementarbeziehungen sind</hi>.</hi> </p><lb/>
            <p>19&#x2019;. <hi rendition="#et"><hi rendition="#i">&#x03B2;</hi> = <hi rendition="#i">&#x03B2;</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi></hi> = (<hi rendition="#i">A</hi> + <hi rendition="#i">B</hi><hi rendition="#sub">1</hi> = 1) (<hi rendition="#i">A B</hi> &#x2260; 0) (<hi rendition="#i">A B</hi><hi rendition="#sub">1</hi> &#x2260; 0)</hi></p><lb/>
            <p>20&#x2019;. <hi rendition="#et"><hi rendition="#i">&#x03B2;</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi></hi> = (<hi rendition="#i">A</hi> + <hi rendition="#i">B</hi> = 1) (<hi rendition="#i">A B</hi> &#x2260; 0) (<hi rendition="#i">A B</hi><hi rendition="#sub">1</hi> &#x2260; 0)</hi></p><lb/>
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[352/0376] Dreiundzwanzigste Vorlesung. 81’. e1A, B1 = f1A1, B = (A1 + B1 = 1) + (A1 B1 ≠ 0) 91’. f1A, B1 = e1A1, B = (A + B = 1) + (A B ≠ 0) 101’. f1 = f1A, B = e1A1, B1 = (A + B1 = 1) + (A B1 ≠ 0). Beziehungen, welche zugleich Grund-, Elementar- und primitive Beziehungen sind (zusammen mit ihren Negationen die 8 Beziehungen De Morgan’s). 11’. a = aA, B = cA, B1 = bA1, B = lA1, B1 = (A1 + B1 = 1) 12’. c = cA, B = aA, B1 = bA1, B1 = lA1, B = (A1 + B = 1) 13’. b = bA, B = aA1, B = cA1, B1 = lA, B1 = (A + B1 = 1) 14’. l = lA, B = aA1, B1 = cA1, B = bA, B1 = (A + B = 1) Negationen derselben. 111’. a1 = a1A, B = c1A, B1 = b1A1, B = l1A1, B1 = (A B ≠ 0) 121’. c1 = c1A, B = a1A, B1 = b1A1, B1 = l1A1, B = (A B1 ≠ 0) 131’. b1 = b1A, B = a1A1, B = c1A1, B1 = l1A, B1 = (A1 B ≠ 0) 141’. l1 = l1A, B = a1A1, B1 = c1A1, B = b1A, B1 = (A1 B1 ≠ 0) (Nicht-primitive, resp.) Die übrigen Beziehungen, welche zu- gleich Grund- und Elementarbeziehungen sind. 15’. g = gA, B = (A B ≠ 0) (A B1 ≠ 0) (A1 B ≠ 0) = αA, B = α 16’. gA, B1 = (A B ≠ 0) (A B1 ≠ 0) (A1 B1 ≠ 0) = αA, B1 17’. gA1, B = (A B ≠ 0) (A1 B ≠ 0) (A1 B1 ≠ 0) = αA1, B 18’. gA1, B1 = (A B1 ≠ 0) (A1 B ≠ 0) (A1 B1 ≠ 0) = αA1, B1 Verneinungen derselben. 151’. g1 = g1A, B = (A1 + B1 = 1) + (A1 + B = 1) + (A + B1 = 1) = α1A, B = α1 161’. g1A, B1 = (A1 + B1 = 1) + (A1 + B = 1) + (A + B = 1) = α1A, B1 171’. g1A1, B = (A1 + B1 = 1) + (A + B1 = 1) + (A + B = 1) = α1A1, B 181’. g1A1, B1 = (A1 + B = 1) + (A + B1 = 1) + (A + B = 1) = α1A1, B1 Die Beziehungen, welche nur Elementarbeziehungen sind. 19’. β = βA, B = (A + B1 = 1) (A B ≠ 0) (A B1 ≠ 0) 20’. βA, B1 = (A + B = 1) (A B ≠ 0) (A B1 ≠ 0)

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URL zu diesem Werk: https://www.deutschestextarchiv.de/schroeder_logik0201_1891
URL zu dieser Seite: https://www.deutschestextarchiv.de/schroeder_logik0201_1891/376
Zitationshilfe: Schröder, Ernst: Vorlesungen über die Algebra der Logik. Bd. 2, Abt. 1. Leipzig, 1891, S. 352. In: Deutsches Textarchiv <https://www.deutschestextarchiv.de/schroeder_logik0201_1891/376>, abgerufen am 18.02.2025.