Consider the following definitions. integer n is alphic if n = 4k+ 5 for some integer k. Definition. Definition. An integer n is gammic if n = 4k+ 1 for some integer k. Suppose that x is alphic and y is gammic. Prove that x + y is even. Suppose that x is alphic and y is gammic. Then there exists an integer k, such that x = and there exists an integer k₂ such that y = Therefore x+y= ] =²([ so x + y is-Select-v

Let P be some predicate. Check the box next to each scenario in which Vn N, P(n) must be true. P(0) holds and for every natural number k > 0, if P(k) does not hold, then there is some natural number i 0, if P(i) holds for every natural number i

(a) Prove that the following statement is true for all real numbers x, y -1, by using a sequence of equivalences: y = 1-x 1+x if and only if x = 1-y 1+ y (b) Prove that the following statement is true for all positive integers m and n: m and n are multiples of each other if and only if m = n.

discrete mathmatics