Here is a truth table of an implication a implies b and its contrapositive not b implies not a. Also shown are the statements not a or b and not a or not not b:
a | b | not a | not b | a --> b | not b --> not a | not a or b | not a or not not b
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T | T | F | F | T | T | T | T
T | F | F | T | F | F | F | F
F | T | T | F | T | T | T | T
F | F | T | T | T | T | T | T
Note also converse and inverse. Just as an implication is logically equivalent to its contrapositive, the converse of the implication is logically equivalent to its inverse. When considering a proof, the contrapositive may be an easier thing to prove than the original implication, for whatever reason. | 
