19 terms

# Geometry- Logic

Logic vocabulary
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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