Let \( A = \{66, 93, 41, 46, 25, 60\} \).

Select all sets that are subsets of \( A \):

- \( D = \{66, 41, 46, 25, 93, 60\} \)
- \( H = \{60, 46, 66, 25\} \)
- \( F = \{25, 46, 60, 41, 93\} \)
- \( G = \{66, 93, 33, 41, 46\} \)
- \( E = \{25, 16, 41, 66, 46, 60\} \)
- \( C = \{89, 93, 41, 46, 66, 25, 60\} \)

Question

High School

Answer :

SpencerDavis09 SpencerDavis09 · Answer 1 · 2023-11-21T12:28:09-05:00

a) D = {66, 41, 46, 25, 93, 60}; b) H = {60, 46, 66, 25}; and c) F = {25, 46, 60, 41, 93} are the subsets of A.

Check if every element in the proposed subset is also an element of set A:

a) D = {66, 41, 46, 25, 93, 60}

D contains all elements of set A and no additional elements. Thus, D is a subset of A.

b) H = {60, 46, 66, 25}

H contains elements all of which are in set A. Therefore, H is a subset of A.

c) F = {25, 46, 60, 41, 93}

F contains elements all of which are in set A. Thus, F is a subset of A.

d) G = {66, 93, 33, 41, 46}

G contains an element (33) that is not in set A. Therefore, G is not a subset of A.

e) E = {25, 16, 41, 66, 46, 60}

E contains an element (16) that is not in set A. Therefore, E is not a subset of A.

f) C = {89, 93, 41, 46, 66, 25, 60}

C contains an element (89) that is not in set A. Therefore, C is not a subset of A.