examples of contrapositive
Recall that the contrapositive of an implication is the equivalent
implication , which is read: “not implies not ”. The following are examples of the contrapositive and converse
of a logical statement:
- 1.
Let be the statement “it is raining” and let be “the ground is getting wet”. Then the statement “if it is raining then the ground is getting wet” is equivalent to “if the ground is not getting wet then it is not raining”. Notice that these are both true statements. Notice also that the converse would be “if the ground is getting wet then it is raining” (which is not necessarily true!).
- 2.
Let be a function of sets and let be finite. The contrapositive statement of “if is surjective
then is finite” (a true statement) would be the implication “if is not finite then is not surjective” (also a true statement). The converse would be “if is finite then is surjective” (a false statement).