Proof question : 1.)For all integers n, prove that 3n + 1 is even if and only if 5n + 2 is odd.
2.) For any sets A, B and C, prove that (A U (B ∩ C)) ⊆ (A U B) ∩ (A U C). Do not use the set equivalence rules or membership tables.
3.)Given set A = {a, b, c, d} and B = {1, 3, 2, 4, 5}, de?ne a function F whose domain is A and co-domain is B. If it is possible to make the function injective, then you must make it injective. If it is possible to make the function surjective, then you must make it surjective. Show the function as a subset of A B in the space provided below.
F =
(a) Explain why it is a function.
(b) Explain why the function is surjective or why it cannot be.
(c) Explain why the function is injective or why it cannot be.