2. Let f be a function from N to N, where f(n) = {s(n = 1) + 24" if n > 0 1. Let R be a relation on Z defined via (a, b)

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2 Let F Be A Function From N To N Where F N S N 1 24 If N 0 1 Let R Be A Relation On Z Defined Via A B 1 (29.27 KiB) Viewed 24 times

2. Let f be a function from N to N, where f(n) = {s(n = 1) + 24" if n > 0 1. Let R be a relation on Z defined via (a, b) ER+ 5|2a + 3b. Prove that R is an equivalence relation. 1 if n = f Find a non-recursive function g for which (Un)(n E N)(f(n) = g(n)), and then prove it by induction = = 3. Prove by induction that ?n? (21 – 1) = (2n-1). 4. Let f be a function from Z to Z, where f(n) (n+3 if n is odd In-5 if n is even Prove that f is a bijection. 5. Prove by cases that 3.n? + = 2n