Problem 3. [25 points] Let F be the set of all functions from integers to integers. For each of the following relations on F, determine if the relation is reflexive, symmetric, and or transitive
a. [5 points] $\langle f, g \rangle | f(1) = g(1)$
b. [5 points] $\langle f, g \rangle | f(0) = g(0) \text{ or } f(1) = g(1)$
c. [5 points] $\langle f, g \rangle | f(x) - g(x) = 1 \text{ for all } x \in \mathbb{Z}$
d. [5 points] $\langle f, g \rangle | \text{for some } c \in \mathbb{Z}, \text{ for all } x \in \mathbb{Z}, f(x) - g(x) = c$
e. [5 points] $\langle f, g \rangle | f(0) = g(1) \text{ and } f(1) = g(0)$
