Converse (logic)
In logic, if "S" is a statement of the form P implies Q, then the converse of "S" is a statement of the form Q implies P. In general, the verity of "S" says nothing about the verity of its converse.
For example, consider the true statement "If I am a human, then I am mortal." The converse is that statement is "If I am mortal, then I am a human," which is not necessarily true. Mathematicians and logicians also sometimes speak of the converses of statements of different forms; for example, the converse of the statement "All humans are mortal" is "All mortals are human."
A truth table makes it clear that "S" and the converse of "S" are not logically equivalent:
| p | q | p→q | q→p |
|---|---|---|---|
| T | T | T | T |
| T | F | F | T |
| F | T | T | F |
| F | F | T | T |
If the statement "S" and it's converse are equivalent then affirming the consequent is valid. This means P is true if and only if Q is also true.
See also: Inverse, Contrapositive, Affirming the consequent.
Categories: Logic