Question

select the correct answer.
what is a counterexample to this claim?
all perfect squares are even.
a. 4
b. 9
c. 16
d. 36

Explanation:

Step1: Define perfect square

A perfect square is $n^2$ where $n\in\mathbb{Z}$.

Step2: Check evenness of options

• A: $4=2^2$, even
• B: $9=3^2$, odd
• C: $16=4^2$, even
• D: $36=6^2$, even

Step3: Identify counterexample

An odd perfect square disproves the claim. 9 is odd and a perfect square.

Answer:

B. 9