For each of the statements, begin a proof by contraposition and a proof by contradiction. This...

For each of the statements, begin a proof by contraposition and a proof by contradiction. This will include rewriting the statement, writing the assumptions, and writing what needs to be shown. From there, pick one of the two methods and finish the proof.

a) For all integers m and n, if m + n is even the m and n are both even or m and n are both odd.

b) For all integers a, b, and c, if a - bc then a - b. (Recall that the symbol - means “does not divide.”)

c) For all x ∈ Z, if x 2 − 6x + 5 is even, then x is odd.

2) Prove the following statement by contradiction: If a, b, and c are integers and a 2 + b 2 = c 2 , then at least one of a and b is even.

Expert Solution

Colby Messinger answered 1 year ago

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