Functions

$S=(0,1) \cup (1,2) \cup (3,4) \; \text{ and } \; T=\{0,1,2,3\}$Let domain and co-domain of a function $y=f(x)$ are $S$ and $T$ respectively.(A) There are infinitely many elements in domain and four elements in co-domain.$\Rightarrow$ There are infinitely many functions from $S$ to $T$.$\Rightarrow$ Option $(A)$ is correct(B) If number of elements in domain is greater than number of elements in co-domain, then number of strictly increasing function is zero.$\Rightarrow$ Option $(B)$ is incorrect(C) Maximum number of continuous functions $=4 \times 4 \times 4=64$(Every subset $(0,1),(1,2),(3,4)$ has four choices)$\because \; \; 64<120 \Rightarrow$ option $(C)$ is correct.(D) For every point at which $f(x)$ is continuous, $f(x)=0$$\Rightarrow \; \;$ Every continuous function from $S$ to $T$ is differentiable.