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

Conditional Statement

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.
Clouds and Rain


If Clouds, then Rain


If Rain, then Clouds


If No Clouds, then No Rain


If No Rain, then No Clouds

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

Conditional, Converse, Inverse, Contrapositive

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