(a) Show that the relation $S$ in set $\mathbb{R}$ of real numbers defined by $S = \{(a, b) : a \leq b^3, a \in \mathbb{R}, b \in \mathbb{R}\}$ is neither reflexive, nor symmetric, nor transitive. OR (b) Let $R$ be the relation defined in the set $A = \{1, 2, 3, 4, 5, 6, 7\}$ by $R = \{(a, b) : \text{both } a \text{ and } b \text{ are either odd or even}\}$. Show that $R$ is an equivalence relation. Hence, find the elements of equivalence class $[1]$.