(Solved): Problem 1, steps. a, b, c, d, and e please! Thank you Discrete mathematical structures computer sci ...

Problem 1, steps. a, b, c, d, and e please! Thank you

Discrete mathematical structures computer science

Problem 1. [15 points] Which of the following relations on the set of all functions from \( Z \) to \( Z \) are equivalence relations? For each that is not an equivalence relation, what properties of an equivalence relation are lacking? a. \( [3 \) points \( ]\{(f, g) \mid f(1)=g(1)\} \) b. \( [3 \) points \( ]\{(f, g) \mid f(0)=g(0) \) or \( f(1)=g(1)\} \) c. [3 points \( ]\{(f, g) \mid f(x)-g(x)=1 \) for all \( x \in Z\} \) d. [3 points] \( \{(f, g) \mid \) for some \( C \in Z \), for all \( x \in Z, f(x)-g(x)=C\} \) e. \( [3 \) points \( ]\{(f, g) \mid f(0)=g(1) \) and \( f(1)=g(0)\} \)