4. Prove each of the following by contradiction. (You may use the fact that every integer...

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4. Prove each of the following by contradiction. (You may use the fact that every integer must be either odd or even, and cannot be both odd and even.) a) If x EZ and is even, then x is even. b) If a, b E Z and ab is odd, then a and b are both odd. c) If a, b, c E Z and a f bc, then a does not divide either b or c. Ø, then SØ. d) If S is a set and S x S 4. Prove each of the following by contradiction. (You may use the fact that every integer must be either odd or even, and cannot be both odd and even.) a) If x EZ and is even, then x is even. b) If a, b E Z and ab is odd, then a and b are both odd. c) If a, b, c E Z and a f bc, then a does not divide either b or c. Ø, then SØ. d) If S is a set and S x S

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