Difference between revisions of "Template:Logic functions"

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imported>Inductiveload
(typos (iff -> if))
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| A AND B || 0 || 0 || 0 || 1
 
| A AND B || 0 || 0 || 0 || 1
|align=left|Output is true if and only if ([[iff]]) both ''A'' and ''B'' are true.
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|align=left|Output is true if and only if ([[if]]) both ''A'' and ''B'' are true.
 
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| A <math>\not\rightarrow</math> B || 0 || 0 || 1 || 0
 
| A <math>\not\rightarrow</math> B || 0 || 0 || 1 || 0
|align=left|''A'' [[Material nonimplication|doesn't imply]] ''B''. True iff ''A'' but not ''B''.
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|align=left|''A'' [[Material nonimplication|doesn't imply]] ''B''. True if ''A'' but not ''B''.
 
|-
 
|-
 
| A || 0 || 0 || 1 || 1
 
| A || 0 || 0 || 1 || 1
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|-
 
|-
 
| A <math>\not\leftarrow</math> B|| 0 || 1 || 0 || 0
 
| A <math>\not\leftarrow</math> B|| 0 || 1 || 0 || 0
|align=left|''A'' [[Converse nonimplication|is not implied by]] ''B''. True iff not ''A'' but ''B''.
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|align=left|''A'' [[Converse nonimplication|is not implied by]] ''B''. True if not ''A'' but ''B''.
 
|-  
 
|-  
 
| B || 0 || 1 || 0 || 1
 
| B || 0 || 1 || 0 || 1
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|-  
 
|-  
 
| A XOR B || 0 || 1 || 1 || 0
 
| A XOR B || 0 || 1 || 1 || 0
|align=left|True iff ''A'' is not equal to ''B''.
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|align=left|True if ''A'' is not equal to ''B''.
 
|-  
 
|-  
 
| A OR B || 0 || 1 || 1 || 1
 
| A OR B || 0 || 1 || 1 || 1
|align=left|True iff ''A'' is true, or ''B'' is true, or both.
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|align=left|True if ''A'' is true, or ''B'' is true, or both.
 
|-  
 
|-  
 
| A NOR B || 1 || 0 || 0 || 0
 
| A NOR B || 1 || 0 || 0 || 0
|align=left|True iff neither ''A'' nor ''B''.
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|align=left|True if neither ''A'' nor ''B''.
 
|-  
 
|-  
 
| A XNOR B || 1 || 0 || 0 || 1
 
| A XNOR B || 1 || 0 || 0 || 1
|align=left|True iff ''A'' is equal to ''B''.
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|align=left|True if ''A'' is equal to ''B''.
 
|-  
 
|-  
 
| NOT B || 1 || 0 || 1 || 0
 
| NOT B || 1 || 0 || 1 || 0
|align=left|True iff ''B'' is false.
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|align=left|True if ''B'' is false.
 
|-  
 
|-  
 
| A <math>\leftarrow</math> B|| 1 || 0 || 1 || 1
 
| A <math>\leftarrow</math> B|| 1 || 0 || 1 || 1
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|-  
 
|-  
 
| NOT A || 1 || 1 || 0 || 0
 
| NOT A || 1 || 1 || 0 || 0
|align=left|True iff ''A'' is false.
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|align=left|True if ''A'' is false.
 
|-  
 
|-  
 
| A <math>\rightarrow</math> B || 1 || 1 || 0 || 1
 
| A <math>\rightarrow</math> B || 1 || 1 || 0 || 1

Revision as of 08:45, 12 September 2011

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 (if) both A and B are true.
A <math>\not\rightarrow</math> B 0 0 1 0 A doesn't imply B. True if 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 if not A but B.
B 0 1 0 1 True whenever B is true.
A XOR B 0 1 1 0 True if A is not equal to B.
A OR B 0 1 1 1 True if A is true, or B is true, or both.
A NOR B 1 0 0 0 True if neither A nor B.
A XNOR B 1 0 0 1 True if A is equal to B.
NOT B 1 0 1 0 True if 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 if 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.