dine5207 wrote:
Bunuel, why we are considering x=-1 when its nowhere mentioned in options.
I'm not Bunuel but going to answer this one.
The question asks "which of the following MUST be true?"
In order to show that the answer is "E. None", we must present a solution in which we can have \(x,y\) such that \(x^y = 1\),and \(x\neq 0\) and all of I, II, and III are all not true.
The example Bunuel gives here is \(x=-1\) and \(y={\text{any even number}}\). Suppose \(y = 2\). Then \(x^y = (-1)^2 = 1\) and yet all of I, II, and III are all not true.