(a) If $f : R^+ \to R$ is defined as $f(x) = \log_a x$ ($a > 0$ and $a \neq 1$), prove that $f$ is a bijection. ($R^+$ is a set of all positive real numbers.) OR (b) Let $A = \{1, 2, 3\}$ and $B = \{4, 5, 6\}$. A relation $R$ from $A$ to $B$ is defined as $R = \{(x, y) : x + y = 6, x \in A, y \in B\}$. (i) Write all elements of $R$. (ii) Is $R$ a function ? Justify. (iii) Determine domain and range of $R$.