These sets are presented in lists of element form. Write the sets in the form of the set generator

Question

These sets are presented in lists of element form. Write the sets in the form of the set generator

a) {0,3,6,9,12}

b) {-3,-2,-1,0,1,2,3}

So... would the solutions be:

a) {n*3: n=0,1,2,3,4}

b) {n:n ∈ Z}

Answer 1

That's not a very specific prompt, is it? There are so many options.

a. $\{n \in \mathbb N \mid n \le 12,\ 3|n \}$

b. $\{ x-1 \mid x \in \{-2,-1,0,1,2,3,4\}\}$

If you wanted to get really picky, you could just say a. $\{n \mid n \in \{0,3,6,9,12\}\}$ or similar. Your answer (in your question) to part a. is correct, but b. is not. $\mathbb Z$ contains all integers, which that set from part b. certainly does not.