Logic/Implication and equivalence
From Internet Web School
Revision as of UNIQ58764a8b7cef031b-MathJax-2-QINU2
Logic > Implication and equivalence
Contents |
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 |