p → q
“If p is true, then q is true.”
Conditional:
If a number is divisible by 4, then it is even.
q → p
The order of the statements is reversed.
If a number is even, then it is divisible by 4.
⚠️ This is not always true, even if the original conditional is true.
¬p → ¬q
Both the hypothesis and conclusion are negated.
If a number is not divisible by 4, then it is not even.
⚠️ The inverse is not logically equivalent to the original conditional.
¬q → ¬p
Both statements are negated and reversed.
If a number is not even, then it is not divisible by 4.
The contrapositive is always logically equivalent to the original conditional.
| p | q | p → q | q → p | ¬p → ¬q | ¬q → ¬p |
|---|---|---|---|---|---|
| T | T | T | T | T | T |
| T | F | F | T | T | F |
| F | T | T | F | F | T |
| F | F | T | T | T | T |