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# Check whether the following statement is true or not:

q : if x, y are integer such that xy is even, then at least one of x and y is an even integer.

Answer :

Let us Assume that p and q be the statements given by

p: x and y are integers and xy is an even integer.

q: At least one of x and y is even.

Let p be true, then

xy is an even integer. So,

xy = 2(n + 1)

Now,

Let x = 2(k + 1)

Now as x is an even integer, xy = 2(k + 1). y is also an even integer.

Now take x = 2(k + 1) and y = 2(m + 1)

xy = 2(k + 1).2(m + 1) = 2.2(k + 1)(m + 1)

Therefore, it is also true.

Hence, the statement is true.

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