select the correct answer.\nwhat is a counterexample to this claim?\nall perfect squares are even.\na. 4\nb…
select the correct answer.\nwhat is a counterexample to this claim?\nall perfect squares are even.\na. 4\nb. 9\nc. 16\nd. 36
Answer
Explanation:
Step1: Recall perfect square definition
A perfect square is a number that is the square of an integer, i.e., ( n = k^2 ) where ( k ) is an integer.
Step2: Analyze each option
- Option A: ( 4 = 2^2 ), and 4 is even. It supports the claim, not a counterexample.
- Option B: ( 9 = 3^2 ), and 9 is odd (not even). This shows a perfect square that is not even, so it's a counterexample.
- Option C: ( 16 = 4^2 ), and 16 is even. Supports the claim.
- Option D: ( 36 = 6^2 ), and 36 is even. Supports the claim.
Answer:
B. 9