Equivalence
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Equivalence
Equivalence is the logical operation corresponding to "IF AND ONLY IF". It states that two propositions are logically identical in truth value.
Symbols
- p ↔ q (standard notation)
- p ⇔ q (alternative)
- p IFF q (short for "if and only if")
Definition
The equivalence p ↔ q is true if p and q have the same truth value. It is false if their truth values differ.
Truth Table
| p | q | p ↔ q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | T |
Examples
- If p = "2 is even" and q = "4 is divisible by 2",
then p ↔ q is true, since both are true.
- In Python:
p == q(when p and q are booleans) - In Java:
p == q(when p and q are booleans)