Implication
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Implication
Implication is the logical operation corresponding to "IF ... THEN". It expresses that if one proposition holds, then another must also hold.
Symbols
- p → q (standard notation)
- p ⊃ q (alternative)
- IF p THEN q (verbal)
Definition
The implication p → q is false only when p is true and q is false. In all other cases it is true.
Additionally, p → q can be reformed into ¬ p ∨ q
Truth Table
| p | q | p → q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
Examples
- If p = "It rains" and q = "The ground is wet",
then p → q = "If it rains, then the ground is wet".
- In programming, implications are usually built using combinations of operators, e.g. in Python:
(not p) or q.