Schröder, Ernst: Vorlesungen über die Algebra der Logik. Bd. 2, Abt. 1. Leipzig, 1891.§ 37. Produkte und Summen von Grundbeziehungen. XI0. Multiplikationstabelle bei Ausschluss undeutiger Symbole.
Schröder, Algebra der Logik. II. 9
§ 37. Produkte und Summen von Grundbeziehungen. XI0. Multiplikationstabelle bei Ausschluss undeutiger Symbole.
Schröder, Algebra der Logik. II. 9
<TEI> <text> <body> <div n="1"> <div n="2"> <div n="3"> <p> <pb facs="#f0153" n="129"/> <fw place="top" type="header">§ 37. Produkte und Summen von Grundbeziehungen.</fw><lb/> <hi rendition="#c">XI<hi rendition="#sup">0</hi>. <hi rendition="#g">Multiplikationstabelle bei Ausschluss undeutiger Symbole</hi>.</hi><lb/> <table> <row> <cell>———,</cell> <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">b</hi> = <hi rendition="#i">b</hi> = <hi rendition="#i">d</hi> + <hi rendition="#i">e</hi>,</cell> <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">c</hi> = <hi rendition="#i">c</hi> = <hi rendition="#i">d</hi> + <hi rendition="#i">f</hi>,</cell> <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">d</hi> = <hi rendition="#i">d</hi>,</cell> <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">e</hi> = <hi rendition="#i">e</hi>,</cell> <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">f</hi> = <hi rendition="#i">f</hi>,</cell> <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">g</hi> = <hi rendition="#i">g</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">a b</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi>,</cell> <cell>——————,</cell> <cell><hi rendition="#i">b c</hi> = <hi rendition="#i">d</hi>,</cell> <cell><hi rendition="#i">b d</hi> = <hi rendition="#i">d</hi>,</cell> <cell><hi rendition="#i">b e</hi> = <hi rendition="#i">e</hi>,</cell> <cell><hi rendition="#i">b f</hi> = 0,</cell> <cell><hi rendition="#i">b g</hi> = 0,</cell> </row><lb/> <row> <cell><hi rendition="#i">a c</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi>,</cell> <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#i">c</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">g</hi>,</cell> <cell>——————,</cell> <cell><hi rendition="#i">c d</hi> = <hi rendition="#i">d</hi>,</cell> <cell><hi rendition="#i">c e</hi> = 0,</cell> <cell><hi rendition="#i">c f</hi> = <hi rendition="#i">f</hi>,</cell> <cell><hi rendition="#i">c g</hi> = 0,</cell> </row><lb/> <row> <cell><hi rendition="#i">a d</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi>,</cell> <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#i">d</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">b</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">f</hi> + <hi rendition="#i">g</hi>,</cell> <cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">d</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">c</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">e</hi> + <hi rendition="#i">g</hi>,</cell> <cell>——————,</cell> <cell><hi rendition="#i">d e</hi> = 0,</cell> <cell><hi rendition="#i">d f</hi> = 0,</cell> <cell><hi rendition="#i">d g</hi> = 0,</cell> </row><lb/> <row> <cell><hi rendition="#i">a e</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi>,</cell> <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#i">e</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">b</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">f</hi> + <hi rendition="#i">g</hi>,</cell> <cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">e</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">g</hi>,</cell> <cell><hi rendition="#i">d</hi><hi rendition="#sub">1</hi><hi rendition="#i">e</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">b</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">f</hi> + <hi rendition="#i">g</hi>,</cell> <cell>——————,</cell> <cell><hi rendition="#i">e f</hi> = 0,</cell> <cell><hi rendition="#i">e g</hi> = 0,</cell> </row><lb/> <row> <cell><hi rendition="#i">a f</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi>,</cell> <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#i">f</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">g</hi>,</cell> <cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">f</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">c</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">e</hi> + <hi rendition="#i">g</hi>,</cell> <cell><hi rendition="#i">d</hi><hi rendition="#sub">1</hi><hi rendition="#i">f</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">c</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">e</hi> + <hi rendition="#i">g</hi>,</cell> <cell><hi rendition="#i">e</hi><hi rendition="#sub">1</hi><hi rendition="#i">f</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">d</hi> + <hi rendition="#i">g</hi>,</cell> <cell>——————,</cell> <cell><hi rendition="#i">f g</hi> = 0,</cell> </row><lb/> <row> <cell><hi rendition="#i">a g</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi>,</cell> <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#i">g</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">f</hi>,</cell> <cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">g</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">e</hi>,</cell> <cell><hi rendition="#i">d</hi><hi rendition="#sub">1</hi><hi rendition="#i">g</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">e</hi> + <hi rendition="#i">f</hi>,</cell> <cell><hi rendition="#i">e</hi><hi rendition="#sub">1</hi><hi rendition="#i">g</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">d</hi> + <hi rendition="#i">f</hi>,</cell> <cell><hi rendition="#i">f</hi><hi rendition="#sub">1</hi><hi rendition="#i">g</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">d</hi> + <hi rendition="#i">e</hi>,</cell> <cell>——————,</cell> </row><lb/> <row> <cell>———,</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">f</hi> + <hi rendition="#i">g</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">e</hi> + <hi rendition="#i">g</hi>,</cell> <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">d</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">e</hi> + <hi rendition="#i">f</hi> + <hi rendition="#i">g</hi>,</cell> <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">e</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">d</hi> + <hi rendition="#i">f</hi> + <hi rendition="#i">g</hi>,</cell> <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">f</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">d</hi> + <hi rendition="#i">e</hi> + <hi rendition="#i">g</hi>,</cell> <cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#i">g</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">e</hi> + <hi rendition="#i">d</hi> + <hi rendition="#i">f</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">a b</hi> = 0,</cell> <cell>——————,</cell> <cell><hi rendition="#i">b c</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">e</hi>,</cell> <cell><hi rendition="#i">b d</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">e</hi>,</cell> <cell><hi rendition="#i">b e</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">d</hi>,</cell> <cell><hi rendition="#i">b f</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">b</hi> = <hi rendition="#i">d</hi> + <hi rendition="#i">e</hi>,</cell> <cell><hi rendition="#i">b g</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">b</hi> = <hi rendition="#i">d</hi> + <hi rendition="#i">e</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">a c</hi> = 0,</cell> <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#i">c</hi> = <hi rendition="#i">f</hi>,</cell> <cell>——————,</cell> <cell><hi rendition="#i">c d</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">f</hi>,</cell> <cell><hi rendition="#i">c e</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">c</hi> = <hi rendition="#i">d</hi> + <hi rendition="#i">f</hi>,</cell> <cell><hi rendition="#i">c f</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">d</hi>,</cell> <cell><hi rendition="#i">c g</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">c</hi> = <hi rendition="#i">d</hi> + <hi rendition="#i">f</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">a d</hi> = 0,</cell> <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#i">d</hi> = 0,</cell> <cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">d</hi> = 0,</cell> <cell>——————,</cell> <cell><hi rendition="#i">d e</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">d</hi>,</cell> <cell><hi rendition="#i">d f</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">d</hi>,</cell> <cell><hi rendition="#i">d g</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">d</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">a e</hi> = 0,</cell> <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#i">e</hi> = 0,</cell> <cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">e</hi> = <hi rendition="#i">e</hi>,</cell> <cell><hi rendition="#i">d</hi><hi rendition="#sub">1</hi><hi rendition="#i">e</hi> = <hi rendition="#i">e</hi>,</cell> <cell>——————,</cell> <cell><hi rendition="#i">e f</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">e</hi>,</cell> <cell><hi rendition="#i">e g</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">e</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">a f</hi> = 0,</cell> <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#i">f</hi> = <hi rendition="#i">f</hi>,</cell> <cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">f</hi> = 0,</cell> <cell><hi rendition="#i">d</hi><hi rendition="#sub">1</hi><hi rendition="#i">f</hi> = <hi rendition="#i">f</hi>,</cell> <cell><hi rendition="#i">e</hi><hi rendition="#sub">1</hi><hi rendition="#i">f</hi> = <hi rendition="#i">f</hi>,</cell> <cell>——————,</cell> <cell><hi rendition="#i">f g</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">f</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">a g</hi> = 0,</cell> <cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#i">g</hi> = <hi rendition="#i">g</hi>,</cell> <cell><hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#i">g</hi> = <hi rendition="#i">g</hi>,</cell> <cell><hi rendition="#i">d</hi><hi rendition="#sub">1</hi><hi rendition="#i">g</hi> = <hi rendition="#i">g</hi>,</cell> <cell><hi rendition="#i">e</hi><hi rendition="#sub">1</hi><hi rendition="#i">g</hi> = <hi rendition="#i">g</hi>,</cell> <cell><hi rendition="#i">f</hi><hi rendition="#sub">1</hi><hi rendition="#i">g</hi> = <hi rendition="#i">g</hi>,</cell> <cell>——————.</cell> </row><lb/> </table> <fw place="bottom" type="sig"><hi rendition="#k">Schröder</hi>, Algebra der Logik. II. 9</fw><lb/> </p> </div> </div> </div> </body> </text> </TEI> [129/0153]
§ 37. Produkte und Summen von Grundbeziehungen.
XI0. Multiplikationstabelle bei Ausschluss undeutiger Symbole.
———, a1 b = b = d + e, a1 c = c = d + f, a1 d = d, a1 e = e, a1 f = f, a1 g = g,
a b1 = a, ——————, b c = d, b d = d, b e = e, b f = 0, b g = 0,
a c1 = a, b1 c1 = a + g, ——————, c d = d, c e = 0, c f = f, c g = 0,
a d1 = a, b1 d1 = b1 = a + f + g, c1 d1 = c1 = a + e + g, ——————, d e = 0, d f = 0, d g = 0,
a e1 = a, b1 e1 = b1 = a + f + g, c1 e1 = a + g, d1 e1 = b1 = a + f + g, ——————, e f = 0, e g = 0,
a f1 = a, b1 f1 = a + g, c1 f1 = c1 = a + e + g, d1 f1 = c1 = a + e + g, e1 f1 = a + d + g, ——————, f g = 0,
a g1 = a, b1 g1 = a + f, c1 g1 = a + e, d1 g1 = a + e + f, e1 g1 = a + d + f, f1 g1 = a + d + e, ——————,
———, a1 b1 = f + g, a1 c1 = e + g, a1 d1 = e + f + g, a1 e1 = d + f + g, a1 f1 = d + e + g, a1 g1 = e + d + f,
a b = 0, ——————, b c1 = e, b d1 = e, b e1 = d, b f1 = b = d + e, b g1 = b = d + e,
a c = 0, b1 c = f, ——————, c d1 = f, c e1 = c = d + f, c f1 = d, c g1 = c = d + f,
a d = 0, b1 d = 0, c1 d = 0, ——————, d e1 = d, d f1 = d, d g1 = d,
a e = 0, b1 e = 0, c1 e = e, d1 e = e, ——————, e f1 = e, e g1 = e,
a f = 0, b1 f = f, c1 f = 0, d1 f = f, e1 f = f, ——————, f g1 = f,
a g = 0, b1 g = g, c1 g = g, d1 g = g, e1 g = g, f1 g = g, ——————.
Schröder, Algebra der Logik. II. 9
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Zitationshilfe: | Schröder, Ernst: Vorlesungen über die Algebra der Logik. Bd. 2, Abt. 1. Leipzig, 1891, S. 129. In: Deutsches Textarchiv <https://www.deutschestextarchiv.de/schroeder_logik0201_1891/153>, abgerufen am 26.08.2024. |