Logic and logical words

Statements of the form, "IF P THEN Q" are called implications. P is frequently called the hypotheses or antecedent, and Q is called the conclusion or consequent. Other related expressions are:
IF Q THEN P. This is called the converse.
IF {not Q} THEN {not P}. This is called the contrapositive.
IF (not P) THEN (not Q). This is called the inverse.

The truth value of an implication is always the same as its contrapositive. The truth value of the converse and the inverse are always the same. The truth value of an implication and its converse may be different.
The logical universe here is the real numbers.

Maintained by greenfie@math.rutgers.edu and last modified 3/27/2009.