For this homework assignment, an integer n e Z is called even iff (ie Z)n = 21, and n is called odd iff (Ej e Z)n = 2; +1. When asked to show that n is even or odd, you must use the definition. 1. Let n be an integer. Prove that if n is even, then n is even. 2. Let n be an integer. Prove that if n is odd, then n is odd. 3. Use the definition to prove that for all ne N, 4n +7 is odd. 4. Let a,b,c be integers. Prove that for all integers m and n, if alb and alc then al(bm + cn). 5. Prove that for all integers m, if m is odd, then there exists k Z such that m = 8k+1. 6. Prove that for any positive real number 1, we have 1 1+-> 2