# Conditional Statement Logical Equivalence Converse, Inverse and Contrapositive

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## Conditional Statement

If two lines are at Right Angles, then they are Perpendicular

## Logical Equivalence

• Statement If P then Q
• Converse If Q then P
• Inverse If not P then not Q
• Contrapositive If not Q then not P
• Biconditional P Q If & Only If (Iff)

Converse, Inverse, and Contrapositive of a Conditional Statement

• A conditional statement takes the form “If p, then q” where p is the hypothesis (antecedent) while q is the conclusion (consequent) . A conditional statement is also known as an implication.
• If statement is true, contrapositive is true
• If converse is true, inverse is true
• The conditional statement is logically equivalent to its contrapositive.
• Thus, p ⇾ q ≡ ~q ⇾ ~p.
• The converse is logically equivalent to the inverse of the original conditional statement. Therefore, q ⇾ p ≡ ~p ⇾ ~q.

## Conditional

If Clouds, then Rain

## Converse

If Rain, then Clouds

## Inverse

If No Clouds, then No Rain

## Contrapositive

If No Rain, then No Clouds

Two lines are at Right Angles If & Only If they are Perpendicular