How many non-empty subsets of {1, 2, 3, 4, 5} consist entirely of prime numbers? (We form a subset of the group of numbers by choosing some number of them, without regard to order. So, {1, 2, 3} is the same as {3, 1, 2}.)
3 out of 5 elements in the given set are prime; they are 2, 3, and 5. So you are in reality counting the number of subsets of the set {2, 3, 5}, which has \({2}^{3}\)subset, including the empty set. Taking that set out, leaves us with 7subsets. Can you list them? (Hint: there are 3 with only one element, 3 with exactly 2 elements and 1 with three elements.)
