Let a and b be integers. Proof  by contrapositive that a + b is an even number if and only if both a and b are odd or both a and b are even.

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Q: Prove or disprove: For all integers a and b, if a +b is odd, then a is even and b is odd.

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Q: For all integers a, b and c, if a divides b and a divides c, then a divides (4b - 3c). True False

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Q: Prove or disprove:  For all integers a and b, if a+b is even, then a is even and b is even.

A: We disprove this statement by taking a counter example.

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.