Problem Solving

$$If\ \ k^{xy}=1,\ where\ k\ne0,$$ which of the following must be true?

$$I.\ \ k=1$$
$$II.\ \ x=0$$
$$III.\ \ y=0$$

A. I only
B. II only
C. III only
D. I and II
E. None

The OA is E.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

AAPL wrote:$$If\ \ k^{xy}=1,\ where\ k\ne0,$$ which of the following must be true?

$$I.\ \ k=1$$
$$II.\ \ x=0$$
$$III.\ \ y=0$$

A. I only
B. II only
C. III only
D. I and II
E. None

The OA is E.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

Test the statements and see if you can falsify them. The only restriction we have is that 2^(xy) = 1. So long as we meet that condition, we have valid numbers to test.

I. Say k = 2. Well, 2^0 = 1, so clearly, k doesn't have to be 1. I is out.
II Say k = 2, x = 1, and y = 0. We'd have 2^(1*0) = 2^0 = 1. Clearly x doesn't have to be 0. II is out.
III Say k =2, x = 0, and y = 1. Now we'd have 2^*(0*1) = 2^0 = 1. Clearly y doesn't have to be 0. III is out.

The answer is E