Difference between revisions of "Template:Logic functions"
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imported>Inductiveload |
(typos (iff -> if)) |
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| Line 20: | Line 20: | ||
|- | |- | ||
| A AND B || 0 || 0 || 0 || 1 | | A AND B || 0 || 0 || 0 || 1 | ||
| − | |align=left|Output is true if and only if ([[ | + | |align=left|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 <math>\not\rightarrow</math> B || 0 || 0 || 1 || 0 | ||
| − | |align=left|''A'' [[Material nonimplication|doesn't imply]] ''B''. True | + | |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 | ||
| Line 29: | Line 29: | ||
|- | |- | ||
| 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 | + | |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 | ||
| Line 35: | Line 35: | ||
|- | |- | ||
| A XOR B || 0 || 1 || 1 || 0 | | A XOR B || 0 || 1 || 1 || 0 | ||
| − | |align=left|True | + | |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 | + | |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 | + | |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 | + | |align=left|True if ''A'' is equal to ''B''. |
|- | |- | ||
| NOT B || 1 || 0 || 1 || 0 | | NOT B || 1 || 0 || 1 || 0 | ||
| − | |align=left|True | + | |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 | ||
| Line 53: | Line 53: | ||
|- | |- | ||
| NOT A || 1 || 1 || 0 || 0 | | NOT A || 1 || 1 || 0 || 0 | ||
| − | |align=left|True | + | |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. | ||