For each of the statements, begin a proof by contraposition anda proof by contradiction. This will include rewriting thestatement, writing the assumptions, and writing what needs to beshown. From there, pick one of the two methods and finish theproof.
a) For all integers m and n, if m + n is even the m and n areboth even or m and n are both odd.
b) For all integers a, b, and c, if a - bc then a - b. (Recallthat 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, andc are integers and a 2 + b 2 = c 2 , then at least one of a and bis even.
