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

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§ 48. Erweiterte Syllogistik.

21'. bA1, B = (A1 + B1 = 1) (A1 B 0) (A1 B1 0)

22'. bA1, B1 = (A1 + B = 1) (A1 B 0) (A1 B1 0)

23'. g = gA, B = (A1 + B = 1) (A B 0) (A1 B 0)

24'. gA, B1 = (A1 + B1 = 1) (A B1 0) (A1 B1 0)

25'. gA1, B = (A + B = 1) (A B 0) (A1 B 0)

26'. gA1, B1 = (A + B1 = 1) (A B1 0) (A1 B1 0)

27'. d = dA, B = (A B + A1 B1 = 1) (A B 0)

28'. dA, B1 = (A B1 + A1 B = 1) (A B1 0)

29'. dA1, B = (A B1 + A1 B = 1) (A1 B 0)

30'. dA1, B1 = (A B + A1 B1 = 1) (A1 B1 0)

Verneinungen ebendieser.

191'. b1 = b1A, B = (A1 + B1 = 1) + (A1 + B = 1) + (A1 + B 0)

201'. b1A, B1 = (A1 + B1 = 1) + (A1 + B = 1) + (A1 B1 0)

211'. b1A1, B = (A + B1 = 1) + (A + B = 1) + (A B 0)

221'. b1A1, B1 = (A + B1 = 1) + (A + B = 1) + (A B1 0)

231'. g1 = g1A, B = (A1 + B1 = 1) + (A B1 0)

241'. g1A, B1 = (A1 + B = 1) + (A + B = 1) + (A B 0)

251'. g1A1, B = (A1 + B1 = 1) + (A + B1 = 1) + (A1 B1 0)

261'. g1A1, B1 = (A1 + B = 1) + (A + B = 1) + (A1 B 0)

271'. d1 = d1A, B = (A1 + B1 = 1) + (A B1 + A1 B 0)

281'. d1A, B1 = (A1 + B = 1) + (A B + A1 B1 0)

291'. d1A1, B = (A + B1 = 1) + (A B + A1 B1 0)

301'. d1A1, B1 = (A + B = 1) + (A B1 + A1 B 0).

Hiezu ist hervorzuheben, dass die nach A und B unsymmetrischen
Beziehungen als paarweise auftretende wie folgt auf einander zurück-
kommen:
kA, B = hB, A, nA, B = mB, A, eA, B = fB, A, bA, B = cB, A, bA, B = gB, A
(desgleichen, A und B vertauscht), wogegen:
dB, A = dA, B, aB, A = aA, B, lB, A = lA, B, gB, A = gA, B oder aB, A = aA, B,
dB, A = dA, B
symmetrische Beziehungen sind. Und analog auch deren Negationen.

Schröder, Algebra der Logik. II. 23
§ 48. Erweiterte Syllogistik.

21’. βA1, B = (A1 + B1 = 1) (A1 B ≠ 0) (A1 B1 ≠ 0)

22’. βA1, B1 = (A1 + B = 1) (A1 B ≠ 0) (A1 B1 ≠ 0)

23’. γ = γA, B = (A1 + B = 1) (A B ≠ 0) (A1 B ≠ 0)

24’. γA, B1 = (A1 + B1 = 1) (A B1 ≠ 0) (A1 B1 ≠ 0)

25’. γA1, B = (A + B = 1) (A B ≠ 0) (A1 B ≠ 0)

26’. γA1, B1 = (A + B1 = 1) (A B1 ≠ 0) (A1 B1 ≠ 0)

27’. δ = δA, B = (A B + A1 B1 = 1) (A B ≠ 0)

28’. δA, B1 = (A B1 + A1 B = 1) (A B1 ≠ 0)

29’. δA1, B = (A B1 + A1 B = 1) (A1 B ≠ 0)

30’. δA1, B1 = (A B + A1 B1 = 1) (A1 B1 ≠ 0)

Verneinungen ebendieser.

191’. β1 = β1A, B = (A1 + B1 = 1) + (A1 + B = 1) + (A1 + B ≠ 0)

201’. β1A, B1 = (A1 + B1 = 1) + (A1 + B = 1) + (A1 B1 ≠ 0)

211’. β1A1, B = (A + B1 = 1) + (A + B = 1) + (A B ≠ 0)

221’. β1A1, B1 = (A + B1 = 1) + (A + B = 1) + (A B1 ≠ 0)

231’. γ1 = γ1A, B = (A1 + B1 = 1) + (A B1 ≠ 0)

241’. γ1A, B1 = (A1 + B = 1) + (A + B = 1) + (A B ≠ 0)

251’. γ1A1, B = (A1 + B1 = 1) + (A + B1 = 1) + (A1 B1 ≠ 0)

261’. γ1A1, B1 = (A1 + B = 1) + (A + B = 1) + (A1 B ≠ 0)

271’. δ1 = δ1A, B = (A1 + B1 = 1) + (A B1 + A1 B ≠ 0)

281’. δ1A, B1 = (A1 + B = 1) + (A B + A1 B1 ≠ 0)

291’. δ1A1, B = (A + B1 = 1) + (A B + A1 B1 ≠ 0)

301’. δ1A1, B1 = (A + B = 1) + (A B1 + A1 B ≠ 0).

Hiezu ist hervorzuheben, dass die nach A und B unsymmetrischen
Beziehungen als paarweise auftretende wie folgt auf einander zurück-
kommen:
kA, B = hB, A, nA, B = mB, A, eA, B = fB, A, bA, B = cB, A, βA, B = γB, A
(desgleichen, A und B vertauscht), wogegen:
dB, A = dA, B, aB, A = aA, B, lB, A = lA, B, gB, A = gA, B oder αB, A = αA, B,
δB, A = δA, B
symmetrische Beziehungen sind. Und analog auch deren Negationen.

Schröder, Algebra der Logik. II. 23
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            <fw place="top" type="header">§ 48. Erweiterte Syllogistik.</fw><lb/>
            <p>21&#x2019;. <hi rendition="#et"><hi rendition="#i">&#x03B2;</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> &#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></p><lb/>
            <p>22&#x2019;. <hi rendition="#et"><hi rendition="#i">&#x03B2;</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="#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></p><lb/>
            <p>23&#x2019;. <hi rendition="#et"><hi rendition="#i">&#x03B3;</hi> = <hi rendition="#i">&#x03B3;</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> = 1) (<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></p><lb/>
            <p>24&#x2019;. <hi rendition="#et"><hi rendition="#i">&#x03B3;</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 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></p><lb/>
            <p>25&#x2019;. <hi rendition="#et"><hi rendition="#i">&#x03B3;</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 rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">B</hi> &#x2260; 0)</hi></p><lb/>
            <p>26&#x2019;. <hi rendition="#et"><hi rendition="#i">&#x03B3;</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 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>27&#x2019;. <hi rendition="#et"><hi rendition="#i">&#x03B4;</hi> = <hi rendition="#i">&#x03B4;</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi></hi> = (<hi rendition="#i">A B</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 B</hi> &#x2260; 0)</hi></p><lb/>
            <p>28&#x2019;. <hi rendition="#et"><hi rendition="#i">&#x03B4;</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><hi rendition="#sub">1</hi> + <hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">B</hi> = 1) (<hi rendition="#i">A B</hi><hi rendition="#sub">1</hi> &#x2260; 0)</hi></p><lb/>
            <p>29&#x2019;. <hi rendition="#et"><hi rendition="#i">&#x03B4;</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> + <hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">B</hi> = 1) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">B</hi> &#x2260; 0)</hi></p><lb/>
            <p>30&#x2019;. <hi rendition="#et"><hi rendition="#i">&#x03B4;</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="#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> <hi rendition="#c"><hi rendition="#g">Verneinungen ebendieser</hi>.</hi> </p><lb/>
            <p>19<hi rendition="#sub">1</hi>&#x2019;. <hi rendition="#et"><hi rendition="#i">&#x03B2;</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">&#x03B2;</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="#sub">1</hi> + <hi rendition="#i">B</hi> &#x2260; 0)</hi></p><lb/>
            <p>20<hi rendition="#sub">1</hi>&#x2019;. <hi rendition="#et"><hi rendition="#i">&#x03B2;</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="#sub">1</hi> <hi rendition="#i">B</hi><hi rendition="#sub">1</hi> &#x2260; 0)</hi></p><lb/>
            <p>21<hi rendition="#sub">1</hi>&#x2019;. <hi rendition="#et"><hi rendition="#i">&#x03B2;</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><hi rendition="#sub">1</hi> = 1) + (<hi rendition="#i">A</hi> + <hi rendition="#i">B</hi> = 1) + (<hi rendition="#i">A B</hi> &#x2260; 0)</hi></p><lb/>
            <p>22<hi rendition="#sub">1</hi>&#x2019;. <hi rendition="#et"><hi rendition="#i">&#x03B2;</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</hi> + <hi rendition="#i">B</hi> = 1) + (<hi rendition="#i">A B</hi><hi rendition="#sub">1</hi> &#x2260; 0)</hi></p><lb/>
            <p>23<hi rendition="#sub">1</hi>&#x2019;. <hi rendition="#et"><hi rendition="#i">&#x03B3;</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">&#x03B3;</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 B</hi><hi rendition="#sub">1</hi> &#x2260; 0)</hi></p><lb/>
            <p>24<hi rendition="#sub">1</hi>&#x2019;. <hi rendition="#et"><hi rendition="#i">&#x03B3;</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> = 1) + (<hi rendition="#i">A</hi> + <hi rendition="#i">B</hi> = 1) + (<hi rendition="#i">A B</hi> &#x2260; 0)</hi></p><lb/>
            <p>25<hi rendition="#sub">1</hi>&#x2019;. <hi rendition="#et"><hi rendition="#i">&#x03B3;</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="#sub">1</hi> <hi rendition="#i">B</hi><hi rendition="#sub">1</hi> &#x2260; 0)</hi></p><lb/>
            <p>26<hi rendition="#sub">1</hi>&#x2019;. <hi rendition="#et"><hi rendition="#i">&#x03B3;</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> = 1) + (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">B</hi> &#x2260; 0)</hi></p><lb/>
            <p>27<hi rendition="#sub">1</hi>&#x2019;. <hi rendition="#et"><hi rendition="#i">&#x03B4;</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">&#x03B4;</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 B</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">B</hi> &#x2260; 0)</hi></p><lb/>
            <p>28<hi rendition="#sub">1</hi>&#x2019;. <hi rendition="#et"><hi rendition="#i">&#x03B4;</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> = 1) + (<hi rendition="#i">A B</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>29<hi rendition="#sub">1</hi>&#x2019;. <hi rendition="#et"><hi rendition="#i">&#x03B4;</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><hi rendition="#sub">1</hi> = 1) + (<hi rendition="#i">A B</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>30<hi rendition="#sub">1</hi>&#x2019;. <hi rendition="#et"><hi rendition="#i">&#x03B4;</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> = 1) + (<hi rendition="#i">A B</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">B</hi> &#x2260; 0).</hi></p><lb/>
            <p>Hiezu ist hervorzuheben, dass die nach <hi rendition="#i">A</hi> und <hi rendition="#i">B unsymmetrischen</hi><lb/>
Beziehungen als paarweise auftretende wie folgt auf einander zurück-<lb/>
kommen:<lb/><hi rendition="#c"><hi rendition="#i">k</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi></hi> = <hi rendition="#i">h</hi><hi rendition="#sup"><hi rendition="#i">B</hi>, <hi rendition="#i">A</hi></hi>, <hi rendition="#i">n</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi></hi> = <hi rendition="#i">m</hi><hi rendition="#sup"><hi rendition="#i">B</hi>, <hi rendition="#i">A</hi></hi>, <hi rendition="#i">e</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi></hi> = <hi rendition="#i">f</hi><hi rendition="#sup"><hi rendition="#i">B</hi>, <hi rendition="#i">A</hi></hi>, <hi rendition="#i">b</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">B</hi>, <hi rendition="#i">A</hi></hi>, <hi rendition="#i">&#x03B2;</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi></hi> = <hi rendition="#i">&#x03B3;</hi><hi rendition="#sup"><hi rendition="#i">B</hi>, <hi rendition="#i">A</hi></hi></hi><lb/>
(desgleichen, <hi rendition="#i">A</hi> und <hi rendition="#i">B</hi> vertauscht), wogegen:<lb/><hi rendition="#c"><hi rendition="#i">d</hi><hi rendition="#sup"><hi rendition="#i">B</hi>, <hi rendition="#i">A</hi></hi> = <hi rendition="#i">d</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">B</hi>, <hi rendition="#i">A</hi></hi> = <hi rendition="#i">a</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi></hi>, <hi rendition="#i">l</hi><hi rendition="#sup"><hi rendition="#i">B</hi>, <hi rendition="#i">A</hi></hi> = <hi rendition="#i">l</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi></hi>, <hi rendition="#i">g</hi><hi rendition="#sup"><hi rendition="#i">B</hi>, <hi rendition="#i">A</hi></hi> = <hi rendition="#i">g</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi></hi> oder <hi rendition="#i">&#x03B1;</hi><hi rendition="#sup"><hi rendition="#i">B</hi>, <hi rendition="#i">A</hi></hi> = <hi rendition="#i">&#x03B1;</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi></hi>,<lb/><hi rendition="#i">&#x03B4;</hi><hi rendition="#sup"><hi rendition="#i">B</hi>, <hi rendition="#i">A</hi></hi> = <hi rendition="#i">&#x03B4;</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">B</hi></hi></hi><lb/><hi rendition="#i">symmetrische</hi> Beziehungen sind. Und analog auch deren Negationen.</p><lb/>
            <fw place="bottom" type="sig"><hi rendition="#k">Schröder</hi>, Algebra der Logik. II. 23</fw><lb/>
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[353/0377] § 48. Erweiterte Syllogistik. 21’. βA1, B = (A1 + B1 = 1) (A1 B ≠ 0) (A1 B1 ≠ 0) 22’. βA1, B1 = (A1 + B = 1) (A1 B ≠ 0) (A1 B1 ≠ 0) 23’. γ = γA, B = (A1 + B = 1) (A B ≠ 0) (A1 B ≠ 0) 24’. γA, B1 = (A1 + B1 = 1) (A B1 ≠ 0) (A1 B1 ≠ 0) 25’. γA1, B = (A + B = 1) (A B ≠ 0) (A1 B ≠ 0) 26’. γA1, B1 = (A + B1 = 1) (A B1 ≠ 0) (A1 B1 ≠ 0) 27’. δ = δA, B = (A B + A1 B1 = 1) (A B ≠ 0) 28’. δA, B1 = (A B1 + A1 B = 1) (A B1 ≠ 0) 29’. δA1, B = (A B1 + A1 B = 1) (A1 B ≠ 0) 30’. δA1, B1 = (A B + A1 B1 = 1) (A1 B1 ≠ 0) Verneinungen ebendieser. 191’. β1 = β1A, B = (A1 + B1 = 1) + (A1 + B = 1) + (A1 + B ≠ 0) 201’. β1A, B1 = (A1 + B1 = 1) + (A1 + B = 1) + (A1 B1 ≠ 0) 211’. β1A1, B = (A + B1 = 1) + (A + B = 1) + (A B ≠ 0) 221’. β1A1, B1 = (A + B1 = 1) + (A + B = 1) + (A B1 ≠ 0) 231’. γ1 = γ1A, B = (A1 + B1 = 1) + (A B1 ≠ 0) 241’. γ1A, B1 = (A1 + B = 1) + (A + B = 1) + (A B ≠ 0) 251’. γ1A1, B = (A1 + B1 = 1) + (A + B1 = 1) + (A1 B1 ≠ 0) 261’. γ1A1, B1 = (A1 + B = 1) + (A + B = 1) + (A1 B ≠ 0) 271’. δ1 = δ1A, B = (A1 + B1 = 1) + (A B1 + A1 B ≠ 0) 281’. δ1A, B1 = (A1 + B = 1) + (A B + A1 B1 ≠ 0) 291’. δ1A1, B = (A + B1 = 1) + (A B + A1 B1 ≠ 0) 301’. δ1A1, B1 = (A + B = 1) + (A B1 + A1 B ≠ 0). Hiezu ist hervorzuheben, dass die nach A und B unsymmetrischen Beziehungen als paarweise auftretende wie folgt auf einander zurück- kommen: kA, B = hB, A, nA, B = mB, A, eA, B = fB, A, bA, B = cB, A, βA, B = γB, A (desgleichen, A und B vertauscht), wogegen: dB, A = dA, B, aB, A = aA, B, lB, A = lA, B, gB, A = gA, B oder αB, A = αA, B, δB, A = δA, B symmetrische Beziehungen sind. Und analog auch deren Negationen. Schröder, Algebra der Logik. II. 23

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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_1891/377
Zitationshilfe: Schröder, Ernst: Vorlesungen über die Algebra der Logik. Bd. 2, Abt. 1. Leipzig, 1891, S. 353. In: Deutsches Textarchiv <https://www.deutschestextarchiv.de/schroeder_logik0201_1891/377>, abgerufen am 16.07.2024.