Suppose that a and b are odd integers with a ? b. Show there is a unique integer c such that |a ? c| = |b ? c|.

Solution:Step-1: In this problem we need to show that there is a unique integer c such that |a -c| = |b -c|. Given : a and b are odd integers with . NOTE: F(x) = |x| is called the “ Absolute value function”. |x| = x , if |x| = -x , if x < 0 . Step-2: So, |a - c| = |b-c| can be written as : a- c = b - c ………….(1) and a -c = -(b...