Difference between revisions of "Template:Logic functions"

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imported>Inductiveload
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imported>Inductiveload
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| TRUE || 1 || 1 || 1 || 1
 
|align=left|Whatever ''A'' and ''B'', the output is true. [[Tautology_(logic)|Tautology]].
 
|align=left|Whatever ''A'' and ''B'', the output is true. [[Tautology_(logic)|Tautology]].
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[[Category:Mathematics templates|{{PAGENAME}}]]
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[[Category:WikiProject Logic]]
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Revision as of 02:25, 28 January 2009

INPUT A 0 0 1 1 Meaning
B 0 1 0 1
OUTPUT FALSE 0 0 0 0 Whatever A and B, the output is false. Contradiction.
A AND B 0 0 0 1 Output is true if and only if (iff) both A and B are true.
A <math>\not\rightarrow</math> B 0 0 1 0 A doesn't imply B. True iff A but not B.
A 0 0 1 1 True whenever A is true.
A <math>\not\leftarrow</math> B 0 1 0 0 A is not implied by B. True iff not A but B.
B 0 1 0 1 True whenever B is true.
A XOR B 0 1 1 0 True iff A is not equal to B.
A OR B 0 1 1 1 True iff A is true, or B is true, or both.
A NOR B 1 0 0 0 True iff neither A nor B.
A XNOR B 1 0 0 1 True iff A is equal to B.
NOT B 1 0 1 0 True iff B is false.
A <math>\leftarrow</math> B 1 0 1 1 A is implied by B. False if not A but B, otherwise true.
NOT A 1 1 0 0 True iff A is false.
A <math>\rightarrow</math> B 1 1 0 1 A implies B. False if A but not B, otherwise true.
A NAND B 1 1 1 0 A and B are not both true.
TRUE 1 1 1 1 Whatever A and B, the output is true. Tautology.