Question

which value(s) of n would provide a counterexample to this statement? select all that apply. if n is an integer, then ( n^2 ) is even. a) -11 b) -4 c) 6 d) 9 e) 11 f) 20

Explanation:

To find a counterexample to the statement "If \( n \) is an integer, then \( n^2 \) is even," we need to find an integer \( n \) such that \( n^2 \) is odd (since an odd number would contradict the claim that \( n^2 \) is even).

Step 1: Analyze Option A (\( n = -11 \))

Calculate \( n^2 \): \( (-11)^2 = 121 \). 121 is odd. So this is a counterexample.

Step 2: Analyze Option B (\( n = -4 \))

Calculate \( n^2 \): \( (-4)^2 = 16 \). 16 is even. Not a counterexample.

Step 3: Analyze Option C (\( n = 6 \))

Calculate \( n^2 \): \( 6^2 = 36 \). 36 is even. Not a counterexample.

Step 4: Analyze Option D (\( n = 9 \))

Calculate \( n^2 \): \( 9^2 = 81 \). 81 is odd. So this is a counterexample.

Step 5: Analyze Option E (\( n = 11 \))

Calculate \( n^2 \): \( 11^2 = 121 \). 121 is odd. So this is a counterexample.

Step 6: Analyze Option F (\( n = 20 \))

Calculate \( n^2 \): \( 20^2 = 400 \). 400 is even. Not a counterexample.

Answer:

A. -11, D. 9, E. 11