Schröder, Ernst: Vorlesungen über die Algebra der Logik. Bd. 2, Abt. 1. Leipzig, 1891.
<TEI> <text> <body> <div n="1"> <div n="2"> <div n="3"> <table> <pb facs="#f0189" n="165"/> <fw place="top" type="header">§ 39. Die denkbaren Umfangsbeziehungen überhaupt.</fw><lb/> <row> <cell>(<hi rendition="#i">a c b l</hi> = 0)</cell> <cell><hi rendition="#i">a</hi> + <hi rendition="#i">c</hi> + <hi rendition="#i">b</hi> + <hi rendition="#i">l</hi></cell> </row><lb/> <row> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>),</cell> <cell><hi rendition="#i">a</hi> + <hi rendition="#i">c b l</hi>,</cell> </row><lb/> <row> <cell>(<hi rendition="#i">a</hi> + <hi rendition="#i">c</hi> + <hi rendition="#i">b</hi>) <hi rendition="#i">l</hi>,</cell> <cell><hi rendition="#i">a c b</hi> + <hi rendition="#i">l</hi>,</cell> </row><lb/> <row> <cell>(<hi rendition="#i">a</hi> + <hi rendition="#i">c</hi> + <hi rendition="#i">l</hi>) <hi rendition="#i">b</hi>,</cell> <cell><hi rendition="#i">a c l</hi> + <hi rendition="#i">b</hi>,</cell> </row><lb/> <row> <cell>(<hi rendition="#i">a</hi> + <hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>) <hi rendition="#i">c</hi></cell> <cell><hi rendition="#i">a b l</hi> + <hi rendition="#i">c</hi></cell> </row><lb/> <row> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">b l</hi>), <hi rendition="#i">a</hi> (<hi rendition="#i">b</hi> + <hi rendition="#i">c l</hi>), <hi rendition="#i">a</hi> (<hi rendition="#i">l</hi> + <hi rendition="#i">c b</hi>)</cell> <cell><hi rendition="#i">a</hi> + <hi rendition="#i">c</hi> (<hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>), <hi rendition="#i">a</hi> + <hi rendition="#i">b</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">l</hi>), <hi rendition="#i">a</hi> + <hi rendition="#i">l</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">b</hi>),</cell> </row><lb/> <row> <cell>(<hi rendition="#i">a</hi> + <hi rendition="#i">c b</hi>) <hi rendition="#i">l</hi>, (<hi rendition="#i">a</hi> + <hi rendition="#i">c l</hi>) <hi rendition="#i">b</hi>, (<hi rendition="#i">a</hi> + <hi rendition="#i">b l</hi>) <hi rendition="#i">c</hi></cell> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">b</hi>) + <hi rendition="#i">l</hi>, <hi rendition="#i">a</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">l</hi>) + <hi rendition="#i">b</hi>, <hi rendition="#i">a</hi> (<hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>) + <hi rendition="#i">c</hi>,</cell> </row><lb/> <row> <cell>(<hi rendition="#i">a c</hi> + <hi rendition="#i">b</hi>) <hi rendition="#i">l</hi>, (<hi rendition="#i">a c</hi> + <hi rendition="#i">l</hi>) <hi rendition="#i">b</hi>, (<hi rendition="#i">a b</hi> + <hi rendition="#i">c</hi>) <hi rendition="#i">l</hi></cell> <cell>(<hi rendition="#i">a</hi> + <hi rendition="#i">c</hi>) <hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>, (<hi rendition="#i">a</hi> + <hi rendition="#i">c</hi>) <hi rendition="#i">l</hi> + <hi rendition="#i">b</hi>, (<hi rendition="#i">a</hi> + <hi rendition="#i">b</hi>) <hi rendition="#i">c</hi> + <hi rendition="#i">l</hi>,</cell> </row><lb/> <row> <cell>(<hi rendition="#i">a b</hi> + <hi rendition="#i">l</hi>) <hi rendition="#i">c</hi>, (<hi rendition="#i">a l</hi> + <hi rendition="#i">c</hi>) <hi rendition="#i">b</hi>, (<hi rendition="#i">a l</hi> + <hi rendition="#i">b</hi>) <hi rendition="#i">c</hi></cell> <cell>(<hi rendition="#i">a</hi> + <hi rendition="#i">b</hi>) <hi rendition="#i">l</hi> + <hi rendition="#i">c</hi>, (<hi rendition="#i">a</hi> + <hi rendition="#i">l</hi>) <hi rendition="#i">c</hi> + <hi rendition="#i">b</hi>, (<hi rendition="#i">a</hi> + <hi rendition="#i">l</hi>) <hi rendition="#i">b</hi> + <hi rendition="#i">c</hi></cell> </row><lb/> <row> <cell><hi rendition="#i">a c</hi> (<hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>), <hi rendition="#i">a b</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">l</hi>), <hi rendition="#i">a l</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">b</hi>)</cell> <cell><hi rendition="#i">a</hi> + <hi rendition="#i">c</hi> + <hi rendition="#i">b l</hi>, <hi rendition="#i">a</hi> + <hi rendition="#i">b</hi> + <hi rendition="#i">c l</hi>, <hi rendition="#i">a</hi> + <hi rendition="#i">l</hi> + <hi rendition="#i">c b</hi></cell> </row><lb/> <row> <cell>(<hi rendition="#i">a</hi> + <hi rendition="#i">c</hi>) <hi rendition="#i">b l</hi>, (<hi rendition="#i">a</hi> + <hi rendition="#i">b</hi>) <hi rendition="#i">c l</hi>, (<hi rendition="#i">a</hi> + <hi rendition="#i">l</hi>) <hi rendition="#i">c b</hi></cell> <cell><hi rendition="#i">a c</hi> + <hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>, <hi rendition="#i">a c</hi> + <hi rendition="#i">c</hi> + <hi rendition="#i">l</hi>, <hi rendition="#i">a l</hi> + <hi rendition="#i">c</hi> + <hi rendition="#i">b</hi></cell> </row><lb/> <row> <cell>(<hi rendition="#i">a</hi> + <hi rendition="#i">c</hi>) (<hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>), (<hi rendition="#i">a</hi> + <hi rendition="#i">b</hi>) (<hi rendition="#i">c</hi> + <hi rendition="#i">l</hi>), (<hi rendition="#i">a</hi> + <hi rendition="#i">l</hi>) (<hi rendition="#i">c</hi> + <hi rendition="#i">b</hi>)</cell> <cell><hi rendition="#i">a c</hi> + <hi rendition="#i">b l</hi>, <hi rendition="#i">a b</hi> + <hi rendition="#i">c l</hi>, <hi rendition="#i">a l</hi> + <hi rendition="#i">c b</hi></cell> </row><lb/> <row> <cell cols="2"><hi rendition="#i">a</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">b</hi>) + <hi rendition="#i">c b</hi>, <hi rendition="#i">a</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">l</hi>) + <hi rendition="#i">c l</hi>, <hi rendition="#i">a</hi> (<hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>) + <hi rendition="#i">b l</hi>, <hi rendition="#i">c b</hi> + <hi rendition="#i">b l</hi> + <hi rendition="#i">l c</hi></cell> </row><lb/> <row> <cell cols="2"><hi rendition="#i">a</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">b</hi>) + <hi rendition="#i">c l</hi>, <hi rendition="#i">a</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">b</hi>) + <hi rendition="#i">b l</hi>, <hi rendition="#i">a</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">l</hi>) + <hi rendition="#i">c b</hi>, <hi rendition="#i">a</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">l</hi>) + <hi rendition="#i">b l</hi>, <hi rendition="#i">a</hi> (<hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>) + <hi rendition="#i">c b</hi>, <hi rendition="#i">a</hi> (<hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>) + <hi rendition="#i">c l</hi></cell> </row><lb/> <row> <cell cols="2"><hi rendition="#i">a c</hi> + <hi rendition="#i">c b</hi> + <hi rendition="#i">b l</hi>, <hi rendition="#i">a c</hi> + <hi rendition="#i">c l</hi> + <hi rendition="#i">l b</hi>, <hi rendition="#i">a b</hi> + <hi rendition="#i">b c</hi> + <hi rendition="#i">c l</hi>, <hi rendition="#i">a b</hi> + <hi rendition="#i">b l</hi> + <hi rendition="#i">l c</hi>, <hi rendition="#i">a l</hi> + <hi rendition="#i">l c</hi> + <hi rendition="#i">c b</hi>, <hi rendition="#i">a l</hi> + <hi rendition="#i">l b</hi> + <hi rendition="#i">b c</hi></cell> </row><lb/> <row> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">b</hi>) + <hi rendition="#i">c b l</hi>,</cell> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>) + <hi rendition="#i">c b</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">l</hi>) + <hi rendition="#i">c b l</hi>,</cell> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>) + <hi rendition="#i">e l</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>) + <hi rendition="#i">c b l</hi>,</cell> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>) + <hi rendition="#i">b l</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">a c b</hi> + (<hi rendition="#i">c</hi> + <hi rendition="#i">b</hi>) <hi rendition="#i">l</hi>,</cell> <cell>(<hi rendition="#i">a</hi> + <hi rendition="#i">c</hi> + <hi rendition="#i">b</hi>) <hi rendition="#i">l</hi> + <hi rendition="#i">c b</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">a c l</hi> + (<hi rendition="#i">c</hi> + <hi rendition="#i">l</hi>) <hi rendition="#i">b</hi>,</cell> <cell>(<hi rendition="#i">a</hi> + <hi rendition="#i">c</hi> + <hi rendition="#i">l</hi>) <hi rendition="#i">b</hi> + <hi rendition="#i">c l</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">a b l</hi> + (<hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>) <hi rendition="#i">c</hi>,</cell> <cell>(<hi rendition="#i">a</hi> + <hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>) <hi rendition="#i">c</hi> + <hi rendition="#i">b l</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">b l</hi>) + <hi rendition="#i">c b</hi>,</cell> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">b</hi>) + (<hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>) <hi rendition="#i">c</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">b l</hi>) + <hi rendition="#i">c l</hi>,</cell> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">l</hi>) + (<hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>) <hi rendition="#i">c</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">b</hi> + <hi rendition="#i">c l</hi>) + <hi rendition="#i">c b</hi>,</cell> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">b</hi>) + (<hi rendition="#i">c</hi> + <hi rendition="#i">l</hi>) <hi rendition="#i">b</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">b</hi> + <hi rendition="#i">c l</hi>) + <hi rendition="#i">b l</hi>,</cell> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>) + (<hi rendition="#i">c</hi> + <hi rendition="#i">l</hi>) <hi rendition="#i">b</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">l</hi> + <hi rendition="#i">c b</hi>) + <hi rendition="#i">c l</hi>,</cell> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">l</hi>) + (<hi rendition="#i">c</hi> + <hi rendition="#i">b</hi>) <hi rendition="#i">l</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">l</hi> + <hi rendition="#i">c b</hi>) + <hi rendition="#i">b l</hi></cell> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>) + (<hi rendition="#i">c</hi> + <hi rendition="#i">b</hi>) <hi rendition="#i">l</hi></cell> </row><lb/> <row> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">c b</hi> + <hi rendition="#i">b l</hi> + <hi rendition="#i">l c</hi>),</cell> <cell><hi rendition="#i">a</hi> + <hi rendition="#i">c b</hi> + <hi rendition="#i">b l</hi> + <hi rendition="#i">l c</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">a c</hi> (<hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>) + <hi rendition="#i">c b l</hi>,</cell> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">b</hi> + <hi rendition="#i">l</hi>) + <hi rendition="#i">c</hi> + <hi rendition="#i">b l</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">a b</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">l</hi>) + <hi rendition="#i">c b l</hi>,</cell> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">l</hi>) + <hi rendition="#i">b</hi> + <hi rendition="#i">c l</hi>,</cell> </row><lb/> <row> <cell><hi rendition="#i">a l</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">b</hi>) + <hi rendition="#i">c b l</hi></cell> <cell><hi rendition="#i">a</hi> (<hi rendition="#i">c</hi> + <hi rendition="#i">b</hi>) + <hi rendition="#i">l</hi> + <hi rendition="#i">c b</hi></cell> </row><lb/> </table> </div> </div> </div> </body> </text> </TEI> [165/0189]
§ 39. Die denkbaren Umfangsbeziehungen überhaupt.
(a c b l = 0) a + c + b + l
a (c + b + l), a + c b l,
(a + c + b) l, a c b + l,
(a + c + l) b, a c l + b,
(a + b + l) c a b l + c
a (c + b l), a (b + c l), a (l + c b) a + c (b + l), a + b (c + l), a + l (c + b),
(a + c b) l, (a + c l) b, (a + b l) c a (c + b) + l, a (c + l) + b, a (b + l) + c,
(a c + b) l, (a c + l) b, (a b + c) l (a + c) b + l, (a + c) l + b, (a + b) c + l,
(a b + l) c, (a l + c) b, (a l + b) c (a + b) l + c, (a + l) c + b, (a + l) b + c
a c (b + l), a b (c + l), a l (c + b) a + c + b l, a + b + c l, a + l + c b
(a + c) b l, (a + b) c l, (a + l) c b a c + b + l, a c + c + l, a l + c + b
(a + c) (b + l), (a + b) (c + l), (a + l) (c + b) a c + b l, a b + c l, a l + c b
a (c + b) + c b, a (c + l) + c l, a (b + l) + b l, c b + b l + l c
a (c + b) + c l, a (c + b) + b l, a (c + l) + c b, a (c + l) + b l, a (b + l) + c b, a (b + l) + c l
a c + c b + b l, a c + c l + l b, a b + b c + c l, a b + b l + l c, a l + l c + c b, a l + l b + b c
a (c + b) + c b l, a (c + b + l) + c b,
a (c + l) + c b l, a (c + b + l) + e l,
a (b + l) + c b l, a (c + b + l) + b l,
a c b + (c + b) l, (a + c + b) l + c b,
a c l + (c + l) b, (a + c + l) b + c l,
a b l + (b + l) c, (a + b + l) c + b l,
a (c + b l) + c b, a (c + b) + (b + l) c,
a (c + b l) + c l, a (c + l) + (b + l) c,
a (b + c l) + c b, a (c + b) + (c + l) b,
a (b + c l) + b l, a (b + l) + (c + l) b,
a (l + c b) + c l, a (c + l) + (c + b) l,
a (l + c b) + b l a (b + l) + (c + b) l
a (c b + b l + l c), a + c b + b l + l c,
a c (b + l) + c b l, a (b + l) + c + b l,
a b (c + l) + c b l, a (c + l) + b + c l,
a l (c + b) + c b l a (c + b) + l + c b
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