abilash10 wrote:

If x is not equal to 0 and xy=1, then which of the following must be true?

I. x=1

II. x=1 and y=0

III. x=1 or y=0

I only

II only

III only

I and III only

None

Notice that if x=−1 and y is any even number, then (−1)even=1, thus none of the options must be true.

The correct answer is E

option C seems to make perfect sense here though. Could someone please elaborate on this please ?

If x is not equal to 0 and x^y=1, then which of the following must be true?

I. x=1

II. x=1 and y=0

III. x=1 or y=0A. I only

B. II only

C. III only

D. I and III only

E. None

Notice that if x=-1 and y is any even number, then \((-1)^{even}=1\), thus none of the options must be true.

Answer: E.

As for your doubt: Option C is III only: x=1 or y=0. Now, if x=-1 and y=2 (\(x^y=(-1)^2=1\)), then neither x is 1 not y is 0, thus this option is not necessarily true.

Hope it's clear.

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