Final answer:
a) A is a subset of B. b) C is not a subset of A. c) B is a subset of A. d) B and C have no common elements.
Step-by-step explanation:
a) A ⊆ B: In order for A to be a subset of B, every element in A must also be in B. Looking at the sets, we see that A = {0, 2, 3} and B = {2, 3}. All the elements of A, 2 and 3, are also present in B. Therefore, A is a subset of B.
b) C ⊆ A: Similarly, in order for C to be a subset of A, every element in C must also be in A. C = {1, 5, 9}, but none of these elements are present in A. Therefore, C is not a subset of A.
c) B ⊆ A: In this case, B = {2, 3} and A = {0, 2, 3}. All the elements of B, 2 and 3, are also present in A. Therefore, B is a subset of A.
d) B ∩ C = ∅: The intersection of two sets is the set of elements that are present in both sets. B ∩ C means the intersection of B and C. In this case, B = {2, 3} and C = {1, 5, 9}. There are no elements that are common to both sets, so their intersection is an empty set (∅).