Let $S = (0, 1) \cup (1, 2) \cup (3, 4)$ and $T = \{0, 1, 2, 3\}$. Then which of the following statements is(are) true?

$S=(0,1)\cup(1,2)\cup(3,4)$ $T=\{0,1,2,3\}$ $(1)\ \text{infinitely many functions } S\to T$ $(2)\ \text{infinitely many strictly increasing } S\to T$ $(3)\ \#\{\text{continuous}\}\le 120;\quad (4)\ \text{every continuous is differentiable}$ $S \text{ has } 3 \text{ components: } I_1=(0,1),\ I_2=(1,2),\ I_3=(3,4)$ $|T|=4,\quad T \text{ finite (discrete)}$ $(1)\ \#\{f:S\to T\}=4^{|S|},\quad |S|=\infty$ $\Rightarrow (1)\ \textbf{TRUE}$ $(2)\ x<y \Rightarrow f(x)<f(y),\quad f(x)\in T$ $\text{an increasing chain needs distinct values in } T$ $x_1<\dots<x_5 \Rightarrow f(x_1)<\dots<f(x_5)$ $\text{needs } 5 \text{ distinct values, but } |T|=4$ $\#\{\text{increasing}\}=0\ \Rightarrow (2)\ \textbf{FALSE}$ $\text{continuous} \Rightarrow f \text{ constant on each connected component}$ $\text{connected image of connected set is connected}$ $I_1,I_2,I_3 \to 4 \text{ choices each independently}$ $\#\{\text{continuous}\}=4^{3}=64$ $64\le 120\ \Rightarrow (3)\ \textbf{TRUE}$ $(4)\ f \text{ constant on each component} \Rightarrow f'=0$ $S \text{ open} \Rightarrow \text{every point interior} \Rightarrow (4)\ \textbf{TRUE}$ $\text{TRUE: }(1),\ (3),\ (4)$ $\boxed{(1),\ (3),\ (4)}$