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

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

Conditional, Converse, Inverse, Contrapositive

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