Logic/Implication and equivalence
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Logic > Implication and equivalence
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Contents
Overview
Implication(→)
"α→β" is "α implies β." or "if α then β."
0 means false, 1 means true, and ≡ means equivalent.
Case of implication. "P→Q" ≡ "￢P∨Q" ≡ "￢(P∧￢Q)"
| P | Q | P→Q | ￢P | ￢Q | ￢P∨Q | P∧￢Q | ￢（P∧￢Q） |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 |
| 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 |
Equivalence(⇔ or ≡)
Case of equivalence. "P⇔Q" ≡ "(P→Q)∧(Q→P)"
| P | Q | P⇔Q | P→Q | Q→P | （P→Q）∧（Q→P） |
|---|---|---|---|---|---|
| 0 | 0 | 1 | 1 | 1 | 1 |
| 0 | 1 | 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 | 0 |
| 1 | 1 | 1 | 1 | 1 | 1 |
