Define $h\colon \mathbb{Z}/\sim ~16 \to \mathbb{Z}/\sim 24$ by $h([a]16) = [3a]24$
a. Prove $h$ is well defined.
b. Compute $h(a)$ where $a = \{[0]16, [3]16, [6]16\}$.
c. Compute $h^{-1}([10]24)$
Is the following correct:
a. $h$ is well defined since each for all $a$ $|h([a]16)|\equiv 1$.
b. $\{[0]24, [9]24, [18]24\}$
c. $\emptyset$