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
-------------------------------------------------------------------------------------
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.