Question

Let x and y be integers. If x²(y+1) is even, then x is ________ or y is ________.

1) even, odd
2) odd, even
3) even, even
4) odd, odd

Answer 1

If x²(y+1) is even, then x is even or y is odd.

Step-by-step explanation:

If x²(y+1) is even, then either x is even or y is odd.

To understand this, let's consider a few cases:

1. If x is even, then x² will be even. And if y is odd, then (y+1) will be even. So, the product x²(y+1) will be even.
2. If x is odd, then x² will be odd. But no matter whether y is odd or even, (y+1) will be odd. So, the product x²(y+1) will be odd.

Therefore, in all possible cases, if x²(y+1) is even, then x is even and y is odd.