Is M a finite set?

Question

If:

i) $f$, $g$, $h$ are functions $\mathbb{R} \to \mathbb{R}$ (domain of the functions is $\mathbb{R}$ and the range is a subset of $\mathbb{R}$),

ii) $A = \{x ∈ \mathbb{R}; f(x)≠g(x)\}$ is a finite set, $B = \{x ∈ \mathbb{R}; g(x)≠h(x)\}$ is a finite set,

Is $M = \{x ∈ \mathbb{R}; f(x)≠h(x)\}$ also a finite set?

Answer 1

Hint: Show that $M\subseteq A\cup B$.