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Conditional Statements

A statement written in theif-thenform is a conditional statement.

p q represents the conditional statement

“if p then q .”

Example 1:

If two angles areadjacent, then they have a common side.

The part of the statement followingifis called thehypothesis, and the part followingthenis called the conclusion.

If two angles are adjacent, Hypothesis then they have a common side . Conclusion

Example 2:

Identify the hypothesis and conclusion of the following statement.

Apolygonis a pentagon, if it has five sides.

Hypothesis: The polygon has five sides.

Conclusion: It is a pentagon.

Biconditional Statement

A biconditional statement is a combination of a conditional statement and its converse written in theif and only ifform.

Two line segments are congruentif and only ifthey are of equal length.

It is a combination of two conditional statements, “if two line segments are congruent then they are of equal length” and “if two line segments are of equal length then they are congruent.”

A biconditional is true if and only if both the conditionals are true.

Biconditionals are represented by the symbol or .

p q means that p q and q p . That is, p q = ( p q ) ( q p ) .

Example:

Write the two conditional statements associated with the biconditional statement below.

A rectangle is a square if and only if the adjacent sides are congruent.

The associated conditional statements are:

a) If the adjacent sides of a rectangle are congruent then it is a square.

b) If a rectangle is a square then the adjacent sides are congruent.