Question

Suppose that A = {2, 4, 6}, B = {2, 6}, C = {4, 6} and D = {4, 6, 8}. Determine which of these sets are subsets of which other of these sets. Check ALL correct answers below.

1) D ⊆ B
2) D⊆ A
3) B⊆C
4) A⊆B
5) C⊆A
6) B⊆D
7) D⊆C
8) C⊆D
9) A⊆D
10) A⊆C
11) B⊆A

Answer 1

To determine which sets are subsets of which other sets, we need to compare the elements in each set. Based on the comparisons, we can conclude that B is a subset of C, C is a subset of A, B is a subset of D, D is a subset of C, and B is a subset of A.

Step-by-step explanation:

To determine which sets are subsets of which other sets, we can compare the elements in each set.

1. To check if D is a subset of B, we compare the elements in D with the elements in B. Since D contains elements that are not in B (8), D is not a subset of B.
2. To check if D is a subset of A, we compare the elements in D with the elements in A. Since D contains elements that are not in A (8), D is not a subset of A.
3. To check if B is a subset of C, we compare the elements in B with the elements in C. Since B contains all the elements in C, B is a subset of C.
4. To check if A is a subset of B, we compare the elements in A with the elements in B. Since A contains elements that are not in B (8, 10, 12, 14, 16, 18), A is not a subset of B.
5. To check if C is a subset of A, we compare the elements in C with the elements in A. Since C contains all the elements in A, C is a subset of A.
6. To check if B is a subset of D, we compare the elements in B with the elements in D. Since B contains all the elements in D, B is a subset of D.
7. To check if D is a subset of C, we compare the elements in D with the elements in C. Since D contains all the elements in C, D is a subset of C.
8. To check if C is a subset of D, we compare the elements in C with the elements in D. Since C contains elements that are not in D (8), C is not a subset of D.
9. To check if A is a subset of D, we compare the elements in A with the elements in D. Since A contains elements that are not in D (8, 10, 12), A is not a subset of D.
10. To check if A is a subset of C, we compare the elements in A with the elements in C. Since A contains elements that are not in C (10, 12), A is not a subset of C.
11. To check if B is a subset of A, we compare the elements in B with the elements in A. Since B contains all the elements in A, B is a subset of A.