Schröder, Ernst: Vorlesungen über die Algebra der Logik. Bd. 2, Abt. 1. Leipzig, 1891.Achtzehnte Vorlesung. Mit der sich hiernach ergebenden Zerfällung der neu hinzuge- Wir haben dann die Tafeln:
Propositionen.
Achtzehnte Vorlesung. Mit der sich hiernach ergebenden Zerfällung der neu hinzuge- Wir haben dann die Tafeln:
Propositionen.
<TEI> <text> <body> <div n="1"> <div n="2"> <div n="3"> <pb facs="#f0166" n="142"/> <fw place="top" type="header">Achtzehnte Vorlesung.</fw><lb/> <p>Mit der sich hiernach ergebenden Zerfällung der neu hinzuge-<lb/> kommenen oder „zusammengesetzten“ Aussagen wollen wir aber so-<lb/> gleich auch diejenige der bisherigen „ursprünglichen“ Aussagen (soweit<lb/> sie multiplikative Kombinationen von <hi rendition="#g">De Morgan’</hi>schen Propositionen<lb/> sind) rekapitulirend in übersichtlicher Zusammenstellung verbinden, da<lb/> man letztere sonst aus verschiedenen Tafeln erst mühsam zusammen-<lb/> suchen müsste.</p><lb/> <p>Wir haben dann die Tafeln:<lb/><hi rendition="#c">XIX<hi rendition="#sup">0</hi>. <hi rendition="#g">Zerfällung der Binionen De Morgan’</hi>scher <hi rendition="#g">Propositionen</hi>.</hi><lb/><table><row><cell><hi rendition="#i">a c</hi> = <hi rendition="#i">h</hi></cell><cell><hi rendition="#i">a b</hi> = <hi rendition="#i">k</hi></cell><cell><hi rendition="#i">a l</hi> = <hi rendition="#i">l a</hi></cell><cell><hi rendition="#i">c b</hi> = <hi rendition="#i">h k</hi> + <hi rendition="#i">δ</hi></cell></row><lb/><row><cell><hi rendition="#i">a c</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi></cell><cell><hi rendition="#i">a b</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi></cell><cell><hi rendition="#i">a l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">l</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi></cell><cell><hi rendition="#i">c b</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h k</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">γ</hi></cell></row><lb/><row><cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">c</hi> = <hi rendition="#i">γ</hi> + <hi rendition="#i">δ</hi></cell><cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">b</hi> = <hi rendition="#i">β</hi> + <hi rendition="#i">δ</hi></cell><cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">l</hi> = <hi rendition="#i">l a</hi> + <hi rendition="#i">m β</hi> + <hi rendition="#i">n γ</hi> + <hi rendition="#i">m n δ</hi></cell><cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">b</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi> + <hi rendition="#i">β</hi></cell></row><lb/><row><cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">c</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">α</hi> + <hi rendition="#i">β</hi></cell><cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">b</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">α</hi> + <hi rendition="#i">γ</hi></cell><cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">l</hi><hi rendition="#sub">1</hi> <hi rendition="#i">α</hi> + <hi rendition="#i">m</hi><hi rendition="#sub">1</hi> <hi rendition="#i">β</hi> + <hi rendition="#i">n</hi><hi rendition="#sub">1</hi> <hi rendition="#i">γ</hi> + <hi rendition="#i">m</hi><hi rendition="#sub">1</hi> <hi rendition="#i">n</hi><hi rendition="#sub">1</hi> <hi rendition="#i">δ</hi></cell><cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">b</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">α</hi></cell></row><lb/></table> <table><row><cell><hi rendition="#i">c l</hi> = <hi rendition="#i">h n</hi> + <hi rendition="#i">n γ</hi> + <hi rendition="#i">m n δ</hi></cell><cell><hi rendition="#i">b l</hi> = <hi rendition="#i">k m</hi> + <hi rendition="#i">m β</hi> + <hi rendition="#i">m n δ</hi></cell></row><lb/><row><cell><hi rendition="#i">c l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h n</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">n</hi><hi rendition="#sub">1</hi> <hi rendition="#i">γ</hi> + <hi rendition="#i">m</hi><hi rendition="#sub">1</hi> <hi rendition="#i">n</hi><hi rendition="#sub">1</hi> <hi rendition="#i">δ</hi></cell><cell><hi rendition="#i">b l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">k m</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">m</hi><hi rendition="#sub">1</hi> <hi rendition="#i">β</hi> + <hi rendition="#i">m</hi><hi rendition="#sub">1</hi> <hi rendition="#i">n</hi><hi rendition="#sub">1</hi> <hi rendition="#i">δ</hi></cell></row><lb/><row><cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">l</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l a</hi> + <hi rendition="#i">l α</hi> + <hi rendition="#i">m β</hi></cell><cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#i">l</hi> = <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l a</hi> + <hi rendition="#i">l α</hi> + <hi rendition="#i">n γ</hi></cell></row><lb/><row><cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi> + <hi rendition="#i">l</hi><hi rendition="#sub">1</hi> <hi rendition="#i">α</hi> + <hi rendition="#i">m</hi><hi rendition="#sub">1</hi> <hi rendition="#i">β</hi></cell><cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#i">l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi> + <hi rendition="#i">l</hi><hi rendition="#sub">1</hi> <hi rendition="#i">α</hi> + <hi rendition="#i">n</hi><hi rendition="#sub">1</hi> <hi rendition="#i">γ</hi></cell></row><lb/></table> <hi rendition="#c">XX<hi rendition="#sup">0</hi>. <hi rendition="#g">Zerfällung der Ternionen von De Morgan’s<lb/> Propositionen</hi>.</hi><lb/><table><row><cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">c b</hi> = <hi rendition="#i">δ</hi></cell><cell><hi rendition="#i">a c</hi><hi rendition="#sub">1</hi><hi rendition="#i">l</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l a</hi></cell><cell><hi rendition="#i">a b</hi><hi rendition="#sub">1</hi><hi rendition="#i">l</hi> = <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l a</hi></cell><cell><hi rendition="#i">c b l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h k</hi> + <hi rendition="#i">m</hi><hi rendition="#sub">1</hi> <hi rendition="#i">n</hi><hi rendition="#sub">1</hi> <hi rendition="#i">δ</hi></cell></row><lb/><row><cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">c b</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">γ</hi></cell><cell><hi rendition="#i">a c</hi><hi rendition="#sub">1</hi><hi rendition="#i">l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi></cell><cell><hi rendition="#i">a b</hi><hi rendition="#sub">1</hi><hi rendition="#i">l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi></cell><cell><hi rendition="#i">c b</hi><hi rendition="#sub">1</hi><hi rendition="#i">l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">n</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">n</hi><hi rendition="#sub">1</hi> <hi rendition="#i">γ</hi></cell></row><lb/><row><cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">b</hi> = <hi rendition="#i">β</hi></cell><cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">l</hi> = <hi rendition="#i">l α</hi> + <hi rendition="#i">m β</hi></cell><cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#i">l</hi> = <hi rendition="#i">l α</hi> + <hi rendition="#i">n γ</hi></cell><cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">b l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k m</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">m</hi><hi rendition="#sub">1</hi> <hi rendition="#i">β</hi></cell></row><lb/><row><cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">b</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">α</hi></cell><cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">l</hi><hi rendition="#sub">1</hi> <hi rendition="#i">α</hi> + <hi rendition="#i">m</hi><hi rendition="#sub">1</hi> <hi rendition="#i">β</hi></cell><cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#i">l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">l</hi><hi rendition="#sub">1</hi> <hi rendition="#i">α</hi> + <hi rendition="#i">n</hi><hi rendition="#sub">1</hi> <hi rendition="#i">γ</hi></cell><cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#i">l</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">l</hi><hi rendition="#sub">1</hi> <hi rendition="#i">a</hi> + <hi rendition="#i">l</hi><hi rendition="#sub">1</hi> <hi rendition="#i">α</hi></cell></row><lb/><row><cell><hi rendition="#i">a c b</hi> = <hi rendition="#i">h k</hi></cell><cell><hi rendition="#i">a c l</hi> = <hi rendition="#i">h n</hi></cell><cell><hi rendition="#i">a b l</hi> = <hi rendition="#i">k m</hi></cell><cell><hi rendition="#i">c b l</hi> = <hi rendition="#i">m n δ</hi></cell></row><lb/><row><cell><hi rendition="#i">a c b</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h k</hi><hi rendition="#sub">1</hi></cell><cell><hi rendition="#i">a c l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">h n</hi><hi rendition="#sub">1</hi></cell><cell><hi rendition="#i">a b l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">k m</hi><hi rendition="#sub">1</hi></cell><cell><hi rendition="#i">c b</hi><hi rendition="#sub">1</hi><hi rendition="#i">l</hi> = <hi rendition="#i">h n</hi> + <hi rendition="#i">n γ</hi></cell></row><lb/><row><cell><hi rendition="#i">a c</hi><hi rendition="#sub">1</hi><hi rendition="#i">b</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi></cell><cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">c l</hi> = <hi rendition="#i">n γ</hi> + <hi rendition="#i">m n δ</hi></cell><cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">b l</hi> = <hi rendition="#i">m β</hi> + <hi rendition="#i">m n δ</hi></cell><cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">b l</hi> = <hi rendition="#i">k m</hi> + <hi rendition="#i">m β</hi></cell></row><lb/><row><cell><hi rendition="#i">a c</hi><hi rendition="#sub">1</hi><hi rendition="#i">b</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></cell><cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">c l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">n</hi><hi rendition="#sub">1</hi> <hi rendition="#i">γ</hi> + <hi rendition="#i">m</hi><hi rendition="#sub">1</hi> <hi rendition="#i">n</hi><hi rendition="#sub">1</hi> <hi rendition="#i">δ</hi></cell><cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">b l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">m</hi><hi rendition="#sub">1</hi> <hi rendition="#i">β</hi> + <hi rendition="#i">m</hi><hi rendition="#sub">1</hi> <hi rendition="#i">n</hi><hi rendition="#sub">1</hi> <hi rendition="#i">δ</hi></cell><cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#i">l</hi> = <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l a</hi> + <hi rendition="#i">l α</hi></cell></row><lb/></table> </p> </div> </div> </div> </body> </text> </TEI> [142/0166]
Achtzehnte Vorlesung.
Mit der sich hiernach ergebenden Zerfällung der neu hinzuge-
kommenen oder „zusammengesetzten“ Aussagen wollen wir aber so-
gleich auch diejenige der bisherigen „ursprünglichen“ Aussagen (soweit
sie multiplikative Kombinationen von De Morgan’schen Propositionen
sind) rekapitulirend in übersichtlicher Zusammenstellung verbinden, da
man letztere sonst aus verschiedenen Tafeln erst mühsam zusammen-
suchen müsste.
Wir haben dann die Tafeln:
XIX0. Zerfällung der Binionen De Morgan’scher Propositionen.
a c = h a b = k a l = l a c b = h k + δ
a c1 = h1 a a b1 = k1 a a l1 = l1 a c b1 = h k1 + γ
a1 c = γ + δ a1 b = β + δ a1 l = l a + m β + n γ + m n δ c1 b = h1 k + β
a1 c1 = α + β a1 b1 = α + γ a1 l1 = l1 α + m1 β + n1 γ + m1 n1 δ c1 b1 = h1 k1 a + α
c l = h n + n γ + m n δ b l = k m + m β + m n δ
c l1 = h n1 + n1 γ + m1 n1 δ b l1 = k m1 + m1 β + m1 n1 δ
c1 l = h1 l a + l α + m β b1 l = k1 l a + l α + n γ
c1 l1 = h1 l1 a + l1 α + m1 β b1 l1 = k1 l1 a + l1 α + n1 γ
XX0. Zerfällung der Ternionen von De Morgan’s
Propositionen.
a1 c b = δ a c1 l = h1 l a a b1 l = k1 l a c b l1 = h k + m1 n1 δ
a1 c b1 = γ a c1 l1 = h1 l1 a a b1 l1 = k1 l1 a c b1 l1 = h k1 n1 + n1 γ
a1 c1 b = β a1 c1 l = l α + m β a1 b1 l = l α + n γ c1 b l1 = h1 k m1 + m1 β
a1 c1 b1 = α a1 c1 l1 = l1 α + m1 β a1 b1 l1 = l1 α + n1 γ c1 b1 l1 = h1 k1 l1 a + l1 α
a c b = h k a c l = h n a b l = k m c b l = m n δ
a c b1 = h k1 a c l1 = h n1 a b l1 = k m1 c b1 l = h n + n γ
a c1 b = h1 k a1 c l = n γ + m n δ a1 b l = m β + m n δ c1 b l = k m + m β
a c1 b1 = h1 k1 a a1 c l1 = n1 γ + m1 n1 δ a1 b l1 = m1 β + m1 n1 δ c1 b1 l = h1 k1 l a + l α
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Zitationshilfe: | Schröder, Ernst: Vorlesungen über die Algebra der Logik. Bd. 2, Abt. 1. Leipzig, 1891, S. 142. In: Deutsches Textarchiv <https://www.deutschestextarchiv.de/schroeder_logik0201_1891/166>, abgerufen am 26.08.2024. |