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: interior angles on the same side of the transversal and exterior angles on the same side of the transversal are supplementary
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 interior angles on the same side of the transversal and exterior angles on the same side of the transversal are supplementary.
- (Converse: "If Q then P" [P ← Q]) if interior angles on the same side of the transversal and exterior angles on the same side of the transversal are supplementary, then the two lines are parallel.
- (Inverse: "If ~P then ~Q" [~P → ~Q]) if the two lines are NOT parallel, then interior angles on the same side of the transversal and exterior angles on the same side of the transversal are NOT supplementary.
- (Contrapositive: "If ~Q then ~P" [~P ← ~Q]) if interior angles on the same side of the transversal and exterior angles on the same side of the transversal are NOT supplementary, then the two lines are NOT parallel.