1-5 Conditional Statements

Conditional Statement

If-then statement, includes a hypothesis after if and a conclusion after then

If p, then q; p —> q

Converse

Reverses the hypothesis and the conclusion of a conditional

If q, then p; q —> p

Negation

Has the opposite meaning of the original statement; not p (~p)

Inverse

Negate both the hypothesis & conclusion of the original statement.

If not p, then not q; ~p —> ~q

Contrapositive

Negate and reverse both the hypothesis & conclusion of a conditional

If not q, then not p; ~q —> ~p

Biconditional statement

Combination of a conditional (p —> q) and it’s converse (q —> p)

p <—> q; p if and only if q

When p and q have the same truth value, the biconditional is true. When they have opposite truth values, it is false