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

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§ 39. Die Umfangsbeziehungen durch die 4 De Morgan's ausgedrückt.

XVII0. Tafel für die Darstellung sämtlicher bisherigen Um-
fangsbeziehungen zwischen Gebieten
A, B, A1, B1 durch die
vier primitiven Beziehungen
.

XVIIa0. Die auxiliären Relationen.

h = a c, h1 = a1 + c1, k = a b, k1 = a1 + b1,
l = l, l1 = l1,
m = b l, m1 = b1 + l1, n = c l, n1 = c1 + l1.

XVIIb0. Grund- und Elementarbeziehungen für A, B:
a = a, a1 = a1, b = b, b1 = b1, c = c, c1 = c1,
d = d11 = b c, d1 = d111 = b1 + c1,
e = f11 = b c1, e1 = f111 = b1 + c, f = e11 = b1 c, f1 = e111 = b + c1,
g = a = a1 b1 c1, g1 = a1 = a + b + c,
b = a1 b c1, b1 = a + b1 + c, g = a1 b1 c, g1 = a + b + c1,
d = a1 b c, d1 = a + b1 + c1.

XVIIc0. Desgleichen mit Hinzuziehung von A1, B1:

a111 = b101 = c110 = l1,a11 = b01 = c10 = l,
a101 = b111 = c1, a01 = b11 = c,a110 = c111 = b1, a10 = c11 = b,
b110 = c01 = a,b110 = c101 = a1,
d01 = d10 = a l,d101 = d110 = a1 + l1,
e01 = f10 = a1 l, e101 = f110 = a + l1, e10 = f01 = a l1, e110 = f101 = a1 + l,
g01 = a01 = a1 c1 l1, g101 = a101 = a + c + l, g10 = a10 = a1 b1 l1, g110 = a110 = a + b + l,
g11 = a11 = b1 c1 l1,g111 = a111 = b + c + l,
b01 = a1 c1 l, b101 = a + c + l1, b10 = a b1 l1, b110 = a1 + b + l, b11 = b1 c l1, b111 = b + c1 + l,
g01 = a c1 l1, g101 = a1 + c + l, g10 = a1 b1 l, g110 = a + b + l1, g11 = b c1 l1, g111 = b1 + c + l,
d01 = a c1 l, d101 = a1 + c + l1, d10 = a b1 l, d110 = a1 + b + l1, d11 = b c l1, d111 = b1 + c1 + l.
Zwischen den vier primitiven Aussagen a, c, b, l selbst besteht übrigens
eine Relation, nämlich diese:
a1 + c1 + b1 + l1 = i, also auch
a b c l = 0

zufolge des Theorems 34+) und 32).

In der letzteren Fassung unsrer Relation als einer "Inkonsistenz"

§ 39. Die Umfangsbeziehungen durch die 4 De Morgan’s ausgedrückt.

XVII0. Tafel für die Darstellung sämtlicher bisherigen Um-
fangsbeziehungen zwischen Gebieten
A, B, A1, B1 durch die
vier primitiven Beziehungen
.

XVIIa0. Die auxiliären Relationen.

h = a c, h1 = a1 + c1, k = a b, k1 = a1 + b1,
l = l, l1 = l1,
m = b l, m1 = b1 + l1, n = c l, n1 = c1 + l1.

XVIIb0. Grund- und Elementarbeziehungen für A, B:
a = a, a1 = a1, b = b, b1 = b1, c = c, c1 = c1,
d = d11 = b c, d1 = d111 = b1 + c1,
e = f11 = b c1, e1 = f111 = b1 + c, f = e11 = b1 c, f1 = e111 = b + c1,
g = α = a1 b1 c1, g1 = α1 = a + b + c,
β = a1 b c1, β1 = a + b1 + c, γ = a1 b1 c, γ1 = a + b + c1,
δ = a1 b c, δ1 = a + b1 + c1.

XVIIc0. Desgleichen mit Hinzuziehung von A1, B1:

a111 = b101 = c110 = l1,a11 = b01 = c10 = l,
a101 = b111 = c1, a01 = b11 = c,a110 = c111 = b1, a10 = c11 = b,
b110 = c01 = a,b110 = c101 = a1,
d01 = d10 = a l,d101 = d110 = a1 + l1,
e01 = f10 = a1 l, e101 = f110 = a + l1, e10 = f01 = a l1, e110 = f101 = a1 + l,
g01 = α01 = a1 c1 l1, g101 = α101 = a + c + l, g10 = α10 = a1 b1 l1, g110 = α110 = a + b + l,
g11 = α11 = b1 c1 l1,g111 = α111 = b + c + l,
β01 = a1 c1 l, β101 = a + c + l1, β10 = a b1 l1, β110 = a1 + b + l, β11 = b1 c l1, β111 = b + c1 + l,
γ01 = a c1 l1, γ101 = a1 + c + l, γ10 = a1 b1 l, γ110 = a + b + l1, γ11 = b c1 l1, γ111 = b1 + c + l,
δ01 = a c1 l, δ101 = a1 + c + l1, δ10 = a b1 l, δ110 = a1 + b + l1, δ11 = b c l1, δ111 = b1 + c1 + l.
Zwischen den vier primitiven Aussagen a, c, b, l selbst besteht übrigens
eine Relation, nämlich diese:
a1 + c1 + b1 + l1 = i, also auch
a b c l = 0

zufolge des Theorems 34+) und 3̅2̅).

In der letzteren Fassung unsrer Relation als einer „Inkonsistenz“

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            <fw place="top" type="header">§ 39. Die Umfangsbeziehungen durch die 4 <hi rendition="#g">De Morgan&#x2019;</hi>s ausgedrückt.</fw><lb/>
            <p> <hi rendition="#c">XVII<hi rendition="#sup">0</hi>. <hi rendition="#g">Tafel für die Darstellung sämtlicher bisherigen Um-<lb/>
fangsbeziehungen zwischen Gebieten</hi> <hi rendition="#i">A</hi>, <hi rendition="#i">B</hi>, <hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi> <hi rendition="#g">durch die<lb/>
vier primitiven Beziehungen</hi>.</hi> </p><lb/>
            <p> <hi rendition="#c">XVII<hi rendition="#sub">a</hi><hi rendition="#sup">0</hi>. <hi rendition="#g">Die auxiliären Relationen</hi>.</hi> </p><lb/>
            <p> <hi rendition="#et"><hi rendition="#i">h</hi> = <hi rendition="#i">a c</hi>, <hi rendition="#i">h</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">c</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">k</hi> = <hi rendition="#i">a b</hi>, <hi rendition="#i">k</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">b</hi><hi rendition="#sub">1</hi>,<lb/><hi rendition="#i">l</hi> = <hi rendition="#i">l</hi>, <hi rendition="#i">l</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">l</hi><hi rendition="#sub">1</hi>,<lb/><hi rendition="#i">m</hi> = <hi rendition="#i">b l</hi>, <hi rendition="#i">m</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">n</hi> = <hi rendition="#i">c l</hi>, <hi rendition="#i">n</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> </p><lb/>
            <p> <hi rendition="#c">XVII<hi rendition="#sub">b</hi><hi rendition="#sup">0</hi>. <hi rendition="#g">Grund- und Elementarbeziehungen für</hi> <hi rendition="#i">A</hi>, <hi rendition="#i">B</hi>:<lb/><hi rendition="#i">a</hi> = <hi rendition="#i">a</hi>, <hi rendition="#i">a</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">b</hi> = <hi rendition="#i">b</hi>, <hi rendition="#i">b</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">b</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">c</hi> = <hi rendition="#i">c</hi>, <hi rendition="#i">c</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">c</hi><hi rendition="#sub">1</hi>,<lb/><hi rendition="#i">d</hi> = <hi rendition="#i">d</hi><hi rendition="#sup">11</hi> = <hi rendition="#i">b c</hi>, <hi rendition="#i">d</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">d</hi><hi rendition="#sub">1</hi><hi rendition="#sup">11</hi> = <hi rendition="#i">b</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">c</hi><hi rendition="#sub">1</hi>,<lb/><hi rendition="#i">e</hi> = <hi rendition="#i">f</hi><hi rendition="#sup">11</hi> = <hi rendition="#i">b c</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">e</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">f</hi><hi rendition="#sub">1</hi><hi rendition="#sup">11</hi> = <hi rendition="#i">b</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">c</hi>, <hi rendition="#i">f</hi> = <hi rendition="#i">e</hi><hi rendition="#sup">11</hi> = <hi rendition="#i">b</hi><hi rendition="#sub">1</hi> <hi rendition="#i">c</hi>, <hi rendition="#i">f</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">e</hi><hi rendition="#sub">1</hi><hi rendition="#sup">11</hi> = <hi rendition="#i">b</hi> + <hi rendition="#i">c</hi><hi rendition="#sub">1</hi>,<lb/><hi rendition="#i">g</hi> = <hi rendition="#i">&#x03B1;</hi> = <hi rendition="#i">a</hi><hi rendition="#sub">1</hi> <hi rendition="#i">b</hi><hi rendition="#sub">1</hi> <hi rendition="#i">c</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">g</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">&#x03B1;</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">b</hi> + <hi rendition="#i">c</hi>,<lb/><hi rendition="#i">&#x03B2;</hi> = <hi rendition="#i">a</hi><hi rendition="#sub">1</hi> <hi rendition="#i">b c</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">&#x03B2;</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">b</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">c</hi>, <hi rendition="#i">&#x03B3;</hi> = <hi rendition="#i">a</hi><hi rendition="#sub">1</hi> <hi rendition="#i">b</hi><hi rendition="#sub">1</hi> <hi rendition="#i">c</hi>, <hi rendition="#i">&#x03B3;</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">b</hi> + <hi rendition="#i">c</hi><hi rendition="#sub">1</hi>,<lb/><hi rendition="#i">&#x03B4;</hi> = <hi rendition="#i">a</hi><hi rendition="#sub">1</hi> <hi rendition="#i">b c</hi>, <hi rendition="#i">&#x03B4;</hi><hi rendition="#sub">1</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">b</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">c</hi><hi rendition="#sub">1</hi>.</hi> </p><lb/>
            <p><hi rendition="#c">XVII<hi rendition="#sub">c</hi><hi rendition="#sup">0</hi>. <hi rendition="#g">Desgleichen mit Hinzuziehung von</hi> <hi rendition="#i">A</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">B</hi><hi rendition="#sub">1</hi>:</hi><lb/><table><row><cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#sup">11</hi> = <hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#sup">01</hi> = <hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#sup">10</hi> = <hi rendition="#i">l</hi><hi rendition="#sub">1</hi>,</cell><cell><hi rendition="#i">a</hi><hi rendition="#sup">11</hi> = <hi rendition="#i">b</hi><hi rendition="#sup">01</hi> = <hi rendition="#i">c</hi><hi rendition="#sup">10</hi> = <hi rendition="#i">l</hi>,</cell></row><lb/><row><cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#sup">01</hi> = <hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#sup">11</hi> = <hi rendition="#i">c</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">a</hi><hi rendition="#sup">01</hi> = <hi rendition="#i">b</hi><hi rendition="#sup">11</hi> = <hi rendition="#i">c</hi>,</cell><cell><hi rendition="#i">a</hi><hi rendition="#sub">1</hi><hi rendition="#sup">10</hi> = <hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#sup">11</hi> = <hi rendition="#i">b</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">a</hi><hi rendition="#sup">10</hi> = <hi rendition="#i">c</hi><hi rendition="#sup">11</hi> = <hi rendition="#i">b</hi>,</cell></row><lb/><row><cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#sup">10</hi> = <hi rendition="#i">c</hi><hi rendition="#sup">01</hi> = <hi rendition="#i">a</hi>,</cell><cell><hi rendition="#i">b</hi><hi rendition="#sub">1</hi><hi rendition="#sup">10</hi> = <hi rendition="#i">c</hi><hi rendition="#sub">1</hi><hi rendition="#sup">01</hi> = <hi rendition="#i">a</hi><hi rendition="#sub">1</hi>,</cell></row><lb/><row><cell><hi rendition="#i">d</hi><hi rendition="#sup">01</hi> = <hi rendition="#i">d</hi><hi rendition="#sup">10</hi> = <hi rendition="#i">a l</hi>,</cell><cell><hi rendition="#i">d</hi><hi rendition="#sub">1</hi><hi rendition="#sup">01</hi> = <hi rendition="#i">d</hi><hi rendition="#sub">1</hi><hi rendition="#sup">10</hi> = <hi rendition="#i">a</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">l</hi><hi rendition="#sub">1</hi>,</cell></row><lb/><row><cell cols="2"><hi rendition="#i">e</hi><hi rendition="#sup">01</hi> = <hi rendition="#i">f</hi><hi rendition="#sup">10</hi> = <hi rendition="#i">a</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l</hi>, <hi rendition="#i">e</hi><hi rendition="#sub">1</hi><hi rendition="#sup">01</hi> = <hi rendition="#i">f</hi><hi rendition="#sub">1</hi><hi rendition="#sup">10</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">l</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">e</hi><hi rendition="#sup">10</hi> = <hi rendition="#i">f</hi><hi rendition="#sup">01</hi> = <hi rendition="#i">a l</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">e</hi><hi rendition="#sub">1</hi><hi rendition="#sup">10</hi> = <hi rendition="#i">f</hi><hi rendition="#sub">1</hi><hi rendition="#sup">01</hi> = <hi rendition="#i">a</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">l</hi>,</cell></row><lb/><row><cell cols="2"><hi rendition="#i">g</hi><hi rendition="#sup">01</hi> = <hi rendition="#i">&#x03B1;</hi><hi rendition="#sup">01</hi> = <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">g</hi><hi rendition="#sub">1</hi><hi rendition="#sup">01</hi> = <hi rendition="#i">&#x03B1;</hi><hi rendition="#sub">1</hi><hi rendition="#sup">01</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">c</hi> + <hi rendition="#i">l</hi>, <hi rendition="#i">g</hi><hi rendition="#sup">10</hi> = <hi rendition="#i">&#x03B1;</hi><hi rendition="#sup">10</hi> = <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">g</hi><hi rendition="#sub">1</hi><hi rendition="#sup">10</hi> = <hi rendition="#i">&#x03B1;</hi><hi rendition="#sub">1</hi><hi rendition="#sup">10</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>,</cell></row><lb/><row><cell><hi rendition="#i">g</hi><hi rendition="#sup">11</hi> = <hi rendition="#i">&#x03B1;</hi><hi rendition="#sup">11</hi> = <hi rendition="#i">b</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>,</cell><cell><hi rendition="#i">g</hi><hi rendition="#sub">1</hi><hi rendition="#sup">11</hi> = <hi rendition="#i">&#x03B1;</hi><hi rendition="#sub">1</hi><hi rendition="#sup">11</hi> = <hi rendition="#i">b</hi> + <hi rendition="#i">c</hi> + <hi rendition="#i">l</hi>,</cell></row><lb/><row><cell cols="2"><hi rendition="#i">&#x03B2;</hi><hi rendition="#sup">01</hi> = <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">&#x03B2;</hi><hi rendition="#sub">1</hi><hi rendition="#sup">01</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">c</hi> + <hi rendition="#i">l</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">&#x03B2;</hi><hi rendition="#sup">10</hi> = <hi rendition="#i">a b</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">&#x03B2;</hi><hi rendition="#sub">1</hi><hi rendition="#sup">10</hi> = <hi rendition="#i">a</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>, <hi rendition="#i">&#x03B2;</hi><hi rendition="#sup">11</hi> = <hi rendition="#i">b</hi><hi rendition="#sub">1</hi> <hi rendition="#i">c l</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">&#x03B2;</hi><hi rendition="#sub">1</hi><hi rendition="#sup">11</hi> = <hi rendition="#i">b</hi> + <hi rendition="#i">c</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">l</hi>,</cell></row><lb/><row><cell cols="2"><hi rendition="#i">&#x03B3;</hi><hi rendition="#sup">01</hi> = <hi rendition="#i">a c</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">&#x03B3;</hi><hi rendition="#sub">1</hi><hi rendition="#sup">01</hi> = <hi rendition="#i">a</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">c</hi> + <hi rendition="#i">l</hi>, <hi rendition="#i">&#x03B3;</hi><hi rendition="#sup">10</hi> = <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">&#x03B3;</hi><hi rendition="#sub">1</hi><hi rendition="#sup">10</hi> = <hi rendition="#i">a</hi> + <hi rendition="#i">b</hi> + <hi rendition="#i">l</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">&#x03B3;</hi><hi rendition="#sup">11</hi> = <hi rendition="#i">b c</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">&#x03B3;</hi><hi rendition="#sub">1</hi><hi rendition="#sup">11</hi> = <hi rendition="#i">b</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">c</hi> + <hi rendition="#i">l</hi>,</cell></row><lb/><row><cell cols="2"><hi rendition="#i">&#x03B4;</hi><hi rendition="#sup">01</hi> = <hi rendition="#i">a c</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l</hi>, <hi rendition="#i">&#x03B4;</hi><hi rendition="#sub">1</hi><hi rendition="#sup">01</hi> = <hi rendition="#i">a</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">c</hi> + <hi rendition="#i">l</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">&#x03B4;</hi><hi rendition="#sup">10</hi> = <hi rendition="#i">a b</hi><hi rendition="#sub">1</hi> <hi rendition="#i">l</hi>, <hi rendition="#i">&#x03B4;</hi><hi rendition="#sub">1</hi><hi rendition="#sup">10</hi> = <hi rendition="#i">a</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">b</hi> + <hi rendition="#i">l</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">&#x03B4;</hi><hi rendition="#sup">11</hi> = <hi rendition="#i">b c l</hi><hi rendition="#sub">1</hi>, <hi rendition="#i">&#x03B4;</hi><hi rendition="#sub">1</hi><hi rendition="#sup">11</hi> = <hi rendition="#i">b</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">c</hi><hi rendition="#sub">1</hi> + <hi rendition="#i">l</hi>.</cell></row><lb/></table> Zwischen den vier primitiven Aussagen <hi rendition="#i">a</hi>, <hi rendition="#i">c</hi>, <hi rendition="#i">b</hi>, <hi rendition="#i">l</hi> selbst besteht übrigens<lb/>
eine Relation, nämlich diese:<lb/><hi rendition="#c"><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">l</hi><hi rendition="#sub">1</hi> = i, also auch<lb/><hi rendition="#i">a b c l</hi> = 0</hi><lb/>
zufolge des Theorems 34<hi rendition="#sub">+</hi>) und 3&#x0305;2&#x0305;).</p><lb/>
            <p>In der letzteren Fassung unsrer Relation als einer &#x201E;Inkonsistenz&#x201C;<lb/></p>
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[137/0161] § 39. Die Umfangsbeziehungen durch die 4 De Morgan’s ausgedrückt. XVII0. Tafel für die Darstellung sämtlicher bisherigen Um- fangsbeziehungen zwischen Gebieten A, B, A1, B1 durch die vier primitiven Beziehungen. XVIIa0. Die auxiliären Relationen. h = a c, h1 = a1 + c1, k = a b, k1 = a1 + b1, l = l, l1 = l1, m = b l, m1 = b1 + l1, n = c l, n1 = c1 + l1. XVIIb0. Grund- und Elementarbeziehungen für A, B: a = a, a1 = a1, b = b, b1 = b1, c = c, c1 = c1, d = d11 = b c, d1 = d111 = b1 + c1, e = f11 = b c1, e1 = f111 = b1 + c, f = e11 = b1 c, f1 = e111 = b + c1, g = α = a1 b1 c1, g1 = α1 = a + b + c, β = a1 b c1, β1 = a + b1 + c, γ = a1 b1 c, γ1 = a + b + c1, δ = a1 b c, δ1 = a + b1 + c1. XVIIc0. Desgleichen mit Hinzuziehung von A1, B1: a111 = b101 = c110 = l1, a11 = b01 = c10 = l, a101 = b111 = c1, a01 = b11 = c, a110 = c111 = b1, a10 = c11 = b, b110 = c01 = a, b110 = c101 = a1, d01 = d10 = a l, d101 = d110 = a1 + l1, e01 = f10 = a1 l, e101 = f110 = a + l1, e10 = f01 = a l1, e110 = f101 = a1 + l, g01 = α01 = a1 c1 l1, g101 = α101 = a + c + l, g10 = α10 = a1 b1 l1, g110 = α110 = a + b + l, g11 = α11 = b1 c1 l1, g111 = α111 = b + c + l, β01 = a1 c1 l, β101 = a + c + l1, β10 = a b1 l1, β110 = a1 + b + l, β11 = b1 c l1, β111 = b + c1 + l, γ01 = a c1 l1, γ101 = a1 + c + l, γ10 = a1 b1 l, γ110 = a + b + l1, γ11 = b c1 l1, γ111 = b1 + c + l, δ01 = a c1 l, δ101 = a1 + c + l1, δ10 = a b1 l, δ110 = a1 + b + l1, δ11 = b c l1, δ111 = b1 + c1 + l. Zwischen den vier primitiven Aussagen a, c, b, l selbst besteht übrigens eine Relation, nämlich diese: a1 + c1 + b1 + l1 = i, also auch a b c l = 0 zufolge des Theorems 34+) und 3̅2̅). In der letzteren Fassung unsrer Relation als einer „Inkonsistenz“

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XML (TEI P5 inkl. att.linguistic)

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TEI-Header · CMDI · Dublin Core

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Dieses Werk wurde gemäß den DTA-Transkriptionsrichtlinien im Double-Keying-Verfahren von Nicht-Muttersprachlern erfasst und in XML/TEI P5 nach DTA-Basisformat kodiert.




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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_1891/161
Zitationshilfe: Schröder, Ernst: Vorlesungen über die Algebra der Logik. Bd. 2, Abt. 1. Leipzig, 1891, S. 137. In: Deutsches Textarchiv <https://www.deutschestextarchiv.de/schroeder_logik0201_1891/161>, abgerufen am 16.04.2024.