Contrapositive Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Write the contrapositive of: 'If a triangle is equilateral, then all its angles are 60Ā°60Ā°.'

Solution

  1. 1
    Negate both parts: 'not all angles are 60Ā°60Ā°' and 'not equilateral.'
  2. 2
    Swap: 'If not all angles of a triangle are 60Ā°60Ā°, then the triangle is not equilateral.'

Answer

IfĀ aĀ triangleĀ doesĀ notĀ haveĀ allĀ anglesĀ equalĀ toĀ 60Ā°,Ā thenĀ itĀ isĀ notĀ equilateral.\text{If a triangle does not have all angles equal to } 60Ā°, \text{ then it is not equilateral.}
The contrapositive reverses and negates both the hypothesis and conclusion of the original conditional.

About Contrapositive

The contrapositive of a conditional statement Pā‡’QP \Rightarrow Q is Ā¬Qā‡’Ā¬P\neg Q \Rightarrow \neg P, formed by negating both parts and reversing their order ā€” it is always logically equivalent to the original.

Learn more about Contrapositive ā†’

More Contrapositive Examples

Example 1 easy

Form the contrapositive of: 'If [formula] is even, then [formula] is even.'

Example 2 medium

Prove by contrapositive: 'If [formula] is odd, then [formula] is odd.'

Example 4 medium

Write the contrapositive of: 'If [formula] is even, then [formula] is even.'

ā† All Contrapositive Examples Contrapositive Concept