Ananya loves even numbers, so she came up with a game to play with her friend So in order to expose her to even numbers. Ananya and So each select, independently and uniformly at random, a number from [1...2n], where n is a positive integer. We call these numbers a and b respectively. Ananya is very happy when either the sum or the product (or both) of a and b is even. Define events X = “a + b is even,” Y = “a · b is even.” Help Ananya out by determining whether X and Y are independent. Prove your answer.

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