Let R be a relation on the set of all integers such that aRb if and only if a + b is even. To show that R is anti-symmetric, we must prove that O For any integers a and b, if a ‡b, then a + b is odd and b + a is odd O For any integers a and b, if a b, then a + b is even or b + a is even O For any integers a and b, if a + b is even, then b + a is even For any integers a and b, if ab, then a + b is even and b + a is even O For any integers a and b, if a b, then a + b is odd or b + a is odd To show that R is not anti-symmetric, we must find a counterexample satisfies which of the following statement? O For some integers a and b, a ‡ b and a + b is even or b + a is even O For some integers a and b, a + b is even and b + a is odd O For some integers a and b, ab and a + b is odd and b + a is odo For some integers a and b, a b and a + b is odd or b + a is odd O For some integers a and b, ab and a + b is even and b + a is even

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