conditionals

If, then statements, p -> q, p implies q, p only if q

Hypothesis

If part of the conditional

Conclusion

Then part of the conditional

Negations

the opposite of the original statement. (not P)

Counterexamples

A statement figure that proves that a statement is false

Converse

Reverse the order of p and q, (If q then p)

Inverse

nagation of conditional (If not p then not q)

Contrapositive

reverse the order and negate the conditional (if not q, then not p)

Rule 1 of logic

A conditional and its contrapositive have the same truth value

Rule 2 of logic

The converse and the inverse of any conditional have the same truth value

Rule 3 of logic

The truth value of a converse may or may not be the same as that of the conditional

Rule 4 of logic

statements that have the same truth value are logically equivalent

converse of the converse

conditional

inverse of the inverse

conditional

contrapositive of the converse

inverse

biconditional

the joining of the conditional and converse (if p, then q and if q the p) (P<->q)

iff

if and only if

Law of detachement

If the conditional is true an the hypothesis is true then the conclusion is true. (p->q) (1 2 1 2)

law of syllogism

p->q, q->r, conclusion= p->r