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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. $\emptyset$

  • 0
    b) and c) are right (but you should probably show your work if you're turning it in as homework) Part a) isn't quite as simple as what you have there. Ask yourself what $a$ represents, as opposed to $[a]16$.2010-12-05
  • 0
    For a. how about for h of all equivalence classes of Z/~16 there is one equivalence class in Z/~24?2010-12-05

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