Schröder, Ernst: Vorlesungen über die Algebra der Logik. Bd. 2, Abt. 1. Leipzig, 1891.Dreiundzwanzigste Vorlesung. (A1 + C1 = 1) (C1 0) aus 11' · 30', 12' · 28'; (A1 + C = 1) (C 0) " 11' · 29', 12' · 27'; (A + C1 = 1) (C1 0) " 13' · 30', 14' · 28'; (A + C = 1) (C 0) " 13' · 29', 14' · 27'; (A1 + C1 = 1) (A1 C 0) aus 11' · 27', 12' · 29'; (A1 + C = 1) (A1 C1 0) " 11' · 28', 12' · 30'; (A + C1 = 1) (A C 0) " 13' · 27', 14' · 29'; (A + C = 1) (A C1 0) " 13' · 28', 14' · 30'; (A1 + C1 = 1) (A1 C1 0) k' aus 11' · 26', 12' · 24'; (A1 + C = 1) (A1 C 0) k " 11' · 25', 12' · 23'; (A + C1 = 1) (A C1 0) k' " 13' · 26', 14' · 24'; (A + C = 1) (A C 0) k " 13' · 25', 14' · 23'; (A1 + C1 = 1) (A1 C1 0) k' l' aus 21' · 26', 22' · 24'; (A1 + C = 1) (A1 C 0) k l' " 21' · 25', 22' · 23'; (A + C1 = 1) (A C1 0) k' l " 19' · 26', 20' · 24'; (A + C = 1) (A C 0) k l " 19' · 25', 20' · 23'; (A C 0) (A C1 0) (A1 C 0) s = aA, C s aus 15' · 30', 16' · 28'; (A C 0) (A C1 0) (A1 C1 0) r = aA, C1 r " 15' · 29', 16' · 27'; (A C 0) (A1 C 0) (A1 C1 0) n = aA1, C n " 17' · 30', 18' · 28'; (A C1 0) (A1 C 0) (A1 C1 0) m = aA1, C1 m " 17' · 29', 18' · 27'; (A1 + C1 = 1) (A C1 0) (A1 C 0) (A1 C1 0) m r = aA, C aA1, C1 m aus 23' · 29', 24' · 27'; (A1 + C = 1) (A C 0) (A1 C 0) (A1 C1 0) n s = aA, C1 aA1, C n aus 23' · 30', 24' · 28'; (A + C1 = 1) (A C 0) (A C1 0) (A1 C1 0) m r = aA1, C aA, C1r aus 25' · 29', 26' · 27'; (A + C = 1) (A C 0) (A C1 0) (A1 C 0) n s = aA1, C1 aA, C s aus 25' · 30', 26' · 28'; (A C + A1 C1 = 1) (A C 0) (A1 C1 0) n = dA, C dA1, C1 n aus 27' · 30', 28' · 28'; (A C + A1 C1 1) (A C 0) (A1 C1 0) r = dA, C dA1, C1 r " 29' · 29'; Dreiundzwanzigste Vorlesung. (A1 + C1 = 1) (C1 ≠ 0) aus 11’ · 30’, 12’ · 28’; (A1 + C = 1) (C ≠ 0) „ 11’ · 29’, 12’ · 27’; (A + C1 = 1) (C1 ≠ 0) „ 13’ · 30’, 14’ · 28’; (A + C = 1) (C ≠ 0) „ 13’ · 29’, 14’ · 27’; (A1 + C1 = 1) (A1 C ≠ 0) aus 11’ · 27’, 12’ · 29’; (A1 + C = 1) (A1 C1 ≠ 0) „ 11’ · 28’, 12’ · 30’; (A + C1 = 1) (A C ≠ 0) „ 13’ · 27’, 14’ · 29’; (A + C = 1) (A C1 ≠ 0) „ 13’ · 28’, 14’ · 30’; (A1 + C1 = 1) (A1 C1 ≠ 0) ϰ' aus 11’ · 26’, 12’ · 24’; (A1 + C = 1) (A1 C ≠ 0) ϰ „ 11’ · 25’, 12’ · 23’; (A + C1 = 1) (A C1 ≠ 0) ϰ' „ 13’ · 26’, 14’ · 24’; (A + C = 1) (A C ≠ 0) ϰ „ 13’ · 25’, 14’ · 23’; (A1 + C1 = 1) (A1 C1 ≠ 0) ϰ' λ' aus 21’ · 26’, 22’ · 24’; (A1 + C = 1) (A1 C ≠ 0) ϰ λ' „ 21’ · 25’, 22’ · 23’; (A + C1 = 1) (A C1 ≠ 0) ϰ' λ „ 19’ · 26’, 20’ · 24’; (A + C = 1) (A C ≠ 0) ϰ λ „ 19’ · 25’, 20’ · 23’; (A C ≠ 0) (A C1 ≠ 0) (A1 C ≠ 0) σ = αA, C σ aus 15’ · 30’, 16’ · 28’; (A C ≠ 0) (A C1 ≠ 0) (A1 C1 ≠ 0) ϱ = αA, C1 ϱ „ 15’ · 29’, 16’ · 27’; (A C ≠ 0) (A1 C ≠ 0) (A1 C1 ≠ 0) ν = αA1, C ν „ 17’ · 30’, 18’ · 28’; (A C1 ≠ 0) (A1 C ≠ 0) (A1 C1 ≠ 0) μ = αA1, C1 μ „ 17’ · 29’, 18’ · 27’; (A1 + C1 = 1) (A C1 ≠ 0) (A1 C ≠ 0) (A1 C1 ≠ 0) μ ϱ = aA, C αA1, C1 μ aus 23’ · 29’, 24’ · 27’; (A1 + C = 1) (A C ≠ 0) (A1 C ≠ 0) (A1 C1 ≠ 0) ν σ = aA, C1 αA1, C ν aus 23’ · 30’, 24’ · 28’; (A + C1 = 1) (A C ≠ 0) (A C1 ≠ 0) (A1 C1 ≠ 0) μ ϱ = aA1, C αA, C1ϱ aus 25’ · 29’, 26’ · 27’; (A + C = 1) (A C ≠ 0) (A C1 ≠ 0) (A1 C ≠ 0) ν σ = aA1, C1 αA, C σ aus 25’ · 30’, 26’ · 28’; (A C + A1 C1 = 1) (A C ≠ 0) (A1 C1 ≠ 0) ν = δA, C δA1, C1 ν aus 27’ · 30’, 28’ · 28’; (A C + A1 C1 ≠ 1) (A C ≠ 0) (A1 C1 ≠ 0) ϱ = δA, C δA1, C1 ϱ „ 29’ · 29’; <TEI> <text> <body> <div n="1"> <div n="2"> <div n="3"> <pb facs="#f0390" n="366"/> <fw place="top" type="header">Dreiundzwanzigste Vorlesung.</fw><lb/> <list> <item>(<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">C</hi><hi rendition="#sub">1</hi> = 1) (<hi rendition="#i">C</hi><hi rendition="#sub">1</hi> ≠ 0) aus 11’ · 30’, 12’ · 28’;</item><lb/> <item>(<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">C</hi> = 1) (<hi rendition="#i">C</hi> ≠ 0) „ 11’ · 29’, 12’ · 27’;</item><lb/> <item>(<hi rendition="#i">A</hi> + <hi rendition="#i">C</hi><hi rendition="#sub">1</hi> = 1) (<hi rendition="#i">C</hi><hi rendition="#sub">1</hi> ≠ 0) „ 13’ · 30’, 14’ · 28’;</item><lb/> <item>(<hi rendition="#i">A</hi> + <hi rendition="#i">C</hi> = 1) (<hi rendition="#i">C</hi> ≠ 0) „ 13’ · 29’, 14’ · 27’;</item><lb/> <item>(<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">C</hi><hi rendition="#sub">1</hi> = 1) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">C</hi> ≠ 0) aus 11’ · 27’, 12’ · 29’;</item><lb/> <item>(<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">C</hi> = 1) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">C</hi><hi rendition="#sub">1</hi> ≠ 0) „ 11’ · 28’, 12’ · 30’;</item><lb/> <item>(<hi rendition="#i">A</hi> + <hi rendition="#i">C</hi><hi rendition="#sub">1</hi> = 1) (<hi rendition="#i">A C</hi> ≠ 0) „ 13’ · 27’, 14’ · 29’;</item><lb/> <item>(<hi rendition="#i">A</hi> + <hi rendition="#i">C</hi> = 1) (<hi rendition="#i">A C</hi><hi rendition="#sub">1</hi> ≠ 0) „ 13’ · 28’, 14’ · 30’;</item><lb/> <item>(<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">C</hi><hi rendition="#sub">1</hi> = 1) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">C</hi><hi rendition="#sub">1</hi> ≠ 0) <hi rendition="#i">ϰ</hi>' aus 11’ · 26’, 12’ · 24’;</item><lb/> <item>(<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">C</hi> = 1) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">C</hi> ≠ 0) <hi rendition="#i">ϰ</hi> „ 11’ · 25’, 12’ · 23’;</item><lb/> <item>(<hi rendition="#i">A</hi> + <hi rendition="#i">C</hi><hi rendition="#sub">1</hi> = 1) (<hi rendition="#i">A C</hi><hi rendition="#sub">1</hi> ≠ 0) <hi rendition="#i">ϰ</hi>' „ 13’ · 26’, 14’ · 24’;</item><lb/> <item>(<hi rendition="#i">A</hi> + <hi rendition="#i">C</hi> = 1) (<hi rendition="#i">A C</hi> ≠ 0) <hi rendition="#i">ϰ</hi> „ 13’ · 25’, 14’ · 23’;</item><lb/> <item>(<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">C</hi><hi rendition="#sub">1</hi> = 1) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">C</hi><hi rendition="#sub">1</hi> ≠ 0) <hi rendition="#i">ϰ</hi>' <hi rendition="#i">λ</hi>' aus 21’ · 26’, 22’ · 24’;</item><lb/> <item>(<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">C</hi> = 1) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">C</hi> ≠ 0) <hi rendition="#i">ϰ λ</hi>' „ 21’ · 25’, 22’ · 23’;</item><lb/> <item>(<hi rendition="#i">A</hi> + <hi rendition="#i">C</hi><hi rendition="#sub">1</hi> = 1) (<hi rendition="#i">A C</hi><hi rendition="#sub">1</hi> ≠ 0) <hi rendition="#i">ϰ</hi>' <hi rendition="#i">λ</hi> „ 19’ · 26’, 20’ · 24’;</item><lb/> <item>(<hi rendition="#i">A</hi> + <hi rendition="#i">C</hi> = 1) (<hi rendition="#i">A C</hi> ≠ 0) <hi rendition="#i">ϰ λ</hi> „ 19’ · 25’, 20’ · 23’;</item><lb/> <item>(<hi rendition="#i">A C</hi> ≠ 0) (<hi rendition="#i">A C</hi><hi rendition="#sub">1</hi> ≠ 0) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">C</hi> ≠ 0) <hi rendition="#i">σ</hi> = <hi rendition="#i">α</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">C</hi></hi> <hi rendition="#i">σ</hi> aus 15’ · 30’, 16’ · 28’;</item><lb/> <item>(<hi rendition="#i">A C</hi> ≠ 0) (<hi rendition="#i">A C</hi><hi rendition="#sub">1</hi> ≠ 0) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">C</hi><hi rendition="#sub">1</hi> ≠ 0) <hi rendition="#i">ϱ</hi> = <hi rendition="#i">α</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">C</hi><hi rendition="#sub">1</hi></hi> <hi rendition="#i">ϱ</hi> „ 15’ · 29’, 16’ · 27’;</item><lb/> <item>(<hi rendition="#i">A C</hi> ≠ 0) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">C</hi> ≠ 0) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">C</hi><hi rendition="#sub">1</hi> ≠ 0) <hi rendition="#i">ν</hi> = <hi rendition="#i">α</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">C</hi></hi> <hi rendition="#i">ν</hi> „ 17’ · 30’, 18’ · 28’;</item><lb/> <item>(<hi rendition="#i">A C</hi><hi rendition="#sub">1</hi> ≠ 0) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">C</hi> ≠ 0) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">C</hi><hi rendition="#sub">1</hi> ≠ 0) <hi rendition="#i">μ</hi> = <hi rendition="#i">α</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">C</hi><hi rendition="#sub">1</hi></hi> <hi rendition="#i">μ</hi> „ 17’ · 29’, 18’ · 27’;</item><lb/> <item>(<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">C</hi><hi rendition="#sub">1</hi> = 1) (<hi rendition="#i">A C</hi><hi rendition="#sub">1</hi> ≠ 0) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">C</hi> ≠ 0) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">C</hi><hi rendition="#sub">1</hi> ≠ 0) <hi rendition="#i">μ ϱ</hi> = <hi rendition="#i">a</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">C</hi></hi> <hi rendition="#i">α</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">C</hi><hi rendition="#sub">1</hi></hi> <hi rendition="#i">μ</hi> aus<lb/> 23’ · 29’, 24’ · 27’;</item><lb/> <item>(<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">C</hi> = 1) (<hi rendition="#i">A C</hi> ≠ 0) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">C</hi> ≠ 0) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">C</hi><hi rendition="#sub">1</hi> ≠ 0) <hi rendition="#i">ν σ</hi> = <hi rendition="#i">a</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">C</hi><hi rendition="#sub">1</hi></hi> <hi rendition="#i">α</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">C</hi></hi> <hi rendition="#i">ν</hi> aus<lb/> 23’ · 30’, 24’ · 28’;</item><lb/> <item>(<hi rendition="#i">A</hi> + <hi rendition="#i">C</hi><hi rendition="#sub">1</hi> = 1) (<hi rendition="#i">A C</hi> ≠ 0) (<hi rendition="#i">A C</hi><hi rendition="#sub">1</hi> ≠ 0) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">C</hi><hi rendition="#sub">1</hi> ≠ 0) <hi rendition="#i">μ ϱ</hi> = <hi rendition="#i">a</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">C</hi></hi> <hi rendition="#i">α</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">C</hi><hi rendition="#sub">1</hi></hi><hi rendition="#i">ϱ</hi> aus<lb/> 25’ · 29’, 26’ · 27’;</item><lb/> <item>(<hi rendition="#i">A</hi> + <hi rendition="#i">C</hi> = 1) (<hi rendition="#i">A C</hi> ≠ 0) (<hi rendition="#i">A C</hi><hi rendition="#sub">1</hi> ≠ 0) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">C</hi> ≠ 0) <hi rendition="#i">ν σ</hi> = <hi rendition="#i">a</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">C</hi><hi rendition="#sub">1</hi></hi> <hi rendition="#i">α</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">C</hi></hi> <hi rendition="#i">σ</hi> aus<lb/> 25’ · 30’, 26’ · 28’;</item><lb/> <item>(<hi rendition="#i">A C</hi> + <hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">C</hi><hi rendition="#sub">1</hi> = 1) (<hi rendition="#i">A C</hi> ≠ 0) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">C</hi><hi rendition="#sub">1</hi> ≠ 0) <hi rendition="#i">ν</hi> = <hi rendition="#i">δ</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">C</hi></hi> <hi rendition="#i">δ</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">C</hi><hi rendition="#sub">1</hi></hi> <hi rendition="#i">ν</hi> aus 27’ · 30’, 28’ · 28’;</item><lb/> <item>(<hi rendition="#i">A C</hi> + <hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">C</hi><hi rendition="#sub">1</hi> ≠ 1) (<hi rendition="#i">A C</hi> ≠ 0) (<hi rendition="#i">A</hi><hi rendition="#sub">1</hi> <hi rendition="#i">C</hi><hi rendition="#sub">1</hi> ≠ 0) <hi rendition="#i">ϱ</hi> = <hi rendition="#i">δ</hi><hi rendition="#sup"><hi rendition="#i">A</hi>, <hi rendition="#i">C</hi></hi> <hi rendition="#i">δ</hi><hi rendition="#sup"><hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">C</hi><hi rendition="#sub">1</hi></hi> <hi rendition="#i">ϱ</hi> „ 29’ · 29’;</item> </list><lb/> </div> </div> </div> </body> </text> </TEI> [366/0390]
Dreiundzwanzigste Vorlesung.
(A1 + C1 = 1) (C1 ≠ 0) aus 11’ · 30’, 12’ · 28’;
(A1 + C = 1) (C ≠ 0) „ 11’ · 29’, 12’ · 27’;
(A + C1 = 1) (C1 ≠ 0) „ 13’ · 30’, 14’ · 28’;
(A + C = 1) (C ≠ 0) „ 13’ · 29’, 14’ · 27’;
(A1 + C1 = 1) (A1 C ≠ 0) aus 11’ · 27’, 12’ · 29’;
(A1 + C = 1) (A1 C1 ≠ 0) „ 11’ · 28’, 12’ · 30’;
(A + C1 = 1) (A C ≠ 0) „ 13’ · 27’, 14’ · 29’;
(A + C = 1) (A C1 ≠ 0) „ 13’ · 28’, 14’ · 30’;
(A1 + C1 = 1) (A1 C1 ≠ 0) ϰ' aus 11’ · 26’, 12’ · 24’;
(A1 + C = 1) (A1 C ≠ 0) ϰ „ 11’ · 25’, 12’ · 23’;
(A + C1 = 1) (A C1 ≠ 0) ϰ' „ 13’ · 26’, 14’ · 24’;
(A + C = 1) (A C ≠ 0) ϰ „ 13’ · 25’, 14’ · 23’;
(A1 + C1 = 1) (A1 C1 ≠ 0) ϰ' λ' aus 21’ · 26’, 22’ · 24’;
(A1 + C = 1) (A1 C ≠ 0) ϰ λ' „ 21’ · 25’, 22’ · 23’;
(A + C1 = 1) (A C1 ≠ 0) ϰ' λ „ 19’ · 26’, 20’ · 24’;
(A + C = 1) (A C ≠ 0) ϰ λ „ 19’ · 25’, 20’ · 23’;
(A C ≠ 0) (A C1 ≠ 0) (A1 C ≠ 0) σ = αA, C σ aus 15’ · 30’, 16’ · 28’;
(A C ≠ 0) (A C1 ≠ 0) (A1 C1 ≠ 0) ϱ = αA, C1 ϱ „ 15’ · 29’, 16’ · 27’;
(A C ≠ 0) (A1 C ≠ 0) (A1 C1 ≠ 0) ν = αA1, C ν „ 17’ · 30’, 18’ · 28’;
(A C1 ≠ 0) (A1 C ≠ 0) (A1 C1 ≠ 0) μ = αA1, C1 μ „ 17’ · 29’, 18’ · 27’;
(A1 + C1 = 1) (A C1 ≠ 0) (A1 C ≠ 0) (A1 C1 ≠ 0) μ ϱ = aA, C αA1, C1 μ aus
23’ · 29’, 24’ · 27’;
(A1 + C = 1) (A C ≠ 0) (A1 C ≠ 0) (A1 C1 ≠ 0) ν σ = aA, C1 αA1, C ν aus
23’ · 30’, 24’ · 28’;
(A + C1 = 1) (A C ≠ 0) (A C1 ≠ 0) (A1 C1 ≠ 0) μ ϱ = aA1, C αA, C1ϱ aus
25’ · 29’, 26’ · 27’;
(A + C = 1) (A C ≠ 0) (A C1 ≠ 0) (A1 C ≠ 0) ν σ = aA1, C1 αA, C σ aus
25’ · 30’, 26’ · 28’;
(A C + A1 C1 = 1) (A C ≠ 0) (A1 C1 ≠ 0) ν = δA, C δA1, C1 ν aus 27’ · 30’, 28’ · 28’;
(A C + A1 C1 ≠ 1) (A C ≠ 0) (A1 C1 ≠ 0) ϱ = δA, C δA1, C1 ϱ „ 29’ · 29’;
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Zitationshilfe: | Schröder, Ernst: Vorlesungen über die Algebra der Logik. Bd. 2, Abt. 1. Leipzig, 1891, S. 366. In: Deutsches Textarchiv <https://www.deutschestextarchiv.de/schroeder_logik0201_1891/390>, abgerufen am 18.02.2025. |