1. We define the symbol , as follows. Let x and y be integers. We write (x , y) if 3x+ 5y = 7k for some [5]integer k.Prove for integers a, b, c, d that:(a , b) and (c , d) is sufficient for (a + c) , (b + d).
2. Prove that: For all integers n, if n^2 is odd, then n is odd.Hint: You may find it easier to rephrase the claim in another way. Recall that A → B can be rewritten in different ways.