Contrapositive Math Example 4

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

Example 4

medium
Write the contrapositive of: 'If n2n^2 is even, then nn is even.'

Solution

  1. 1
    To form the contrapositive, negate both parts and reverse the direction of the statement.
  2. 2
    The result is: 'If nn is not even (that is, odd), then n2n^2 is not even (that is, odd).'

Answer

If n is odd, then n2 is odd.\text{If } n \text{ is odd, then } n^2 \text{ is odd.}
A statement and its contrapositive are logically equivalent. Reversing without negating would produce the converse instead, which is a different statement.

About Contrapositive

The contrapositive of a conditional statement P⇒QP \Rightarrow Q is ¬Q⇒¬P\neg Q \Rightarrow \neg P, formed by negating both parts and reversing their order — it is always logically equivalent to the original.

Learn more about Contrapositive →

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 3 easy

Write the contrapositive of: 'If a triangle is equilateral, then all its angles are [formula].'

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