I have a question I have been trying to answer which is: Let $A = \{x ∈ \mathbb N | x^2 < 37\}$ and $B = \{3k+1 | k ∈ \{1,2,3,4\}\}$ be sets. List out the elements of A and the elements of B and List all the subsets of B.
My answer for the subsets of $B =$ {∅}, {{1}}, {{2}}, {{3}}, {{4}}, {{1,2,3,4}}, {{1,2,3}}, {{1,3,4}}, {{1,2,4}}, {{1,2}}, {{1,3}}, {{1,4}}, {{2,3,4}}, {{2,3}}, {{2,4}}, {{3,4}}. My answer for the elements of $A = 1,2,3,4,5,6$ My answer for the elements of $B = 1,2,3,4$
Is this correct or am I getting something wrong? I feel uncertain about my answer.
The elements you have listed for set $A$ are correct. The elements in set $B$ are incorrect. For the elements in B, you are looking for numbers in the form $3k+1$, where $k\in\{1,2,3,4\}$, not the values of $k$ itself (ie $3(1) + 1 = 4$, $3(2) + 1 = 6$, etc.)
The way you're finding subsets looks fine to me!