If "P" represents one statement and "Q" represents another statement, then "If P then Q" is called a conditional sentence symbolized as "P → Q"
The following four conditional sentences can be considered:
The biconditional sentence P if and only if Q states that the conditional sentence, its converse, inverse and contrapositive are all true.
Using the biconditional sentence of this example, it is given that "a transversal intersects two lines". The remaining part of the sentence can be broken up into the two parts below.
P: two lines are parallel
Q: alternate angles are congruent
P if and only if Q [i.e. P ↔ Q] results in the following:
When a transversal intersects two lines,:
- (Conditional sentence: "If P then Q" [P → Q]) if the two lines are parallel, then alternate angles are congruent.
- (Converse: "If Q then P" [P ← Q]) if alternate angles are congruent, then the two lines are parallel.
- (Inverse: "If ~P then ~Q" [~P → ~Q]) if the two lines are NOT parallel, then alternate angles are NOT congruent.
- (Contrapositive: "If ~Q then ~P" [~P ← ~Q]) if alternate angles are NOT congruent, then the two lines are NOT parallel.