Logic/Implication and equivalence

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Logic > Implication and equivalence

Contents 1 Contents 2 Overview 2.1 Implication(→) 2.2 Equivalence(⇔ or ≡) 3 CAI Exercise

Contents

• Category:Mathematical logic（Wikipedia）
• Boolean algebra (logic)
• Material conditional
• If and only if

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

CAI Exercise

• Go to CAI Exercise page