You are given a discrete math problem: Let A = {1, 2, 3, 4, ...

Prompt

You are given a discrete math problem: Let A = {1, 2, 3, 4, 5}. Consider relations on A that are symmetric and transitive. (a) How many are not reflexive? (b) How many are neither reflexive nor irreflexive? (A relation is irreflexive if (a, a) ∉ R for every a ∈ A.) (c) How many have (a, a) ∉ R for exactly one element a ∈ A? (d) How many contain (1, 2) but are not reflexive? Justify each answer. Your task is to solve the given problem by providing a clear, step-by-step solution.