Answer :
To identify which of the given sets are subsets of [tex]\( A = \{39, 15, 85, 51, 22, 84\} \)[/tex], we need to check if every element of each set is present in [tex]\( A \)[/tex].
Let's go through each set:
1. Set [tex]\( C = \{85, 84, 22, 39, 15, 51\} \)[/tex]
- Check each element: 85, 84, 22, 39, 15, and 51.
- All elements are in [tex]\( A \)[/tex].
- Therefore, [tex]\( C \)[/tex] is a subset of [tex]\( A \)[/tex].
2. Set [tex]\( F = \{88, 51, 22, 85, 84, 39\} \)[/tex]
- Check each element: 88 is not in [tex]\( A \)[/tex].
- Since 88 is missing from [tex]\( A \)[/tex], [tex]\( F \)[/tex] is not a subset of [tex]\( A \)[/tex].
3. Set [tex]\( G = \{85, 54, 51, 39, 15\} \)[/tex]
- Check each element: 54 is not in [tex]\( A \)[/tex].
- Since 54 is missing from [tex]\( A \)[/tex], [tex]\( G \)[/tex] is not a subset of [tex]\( A \)[/tex].
4. Set [tex]\( D = \{39, 51, 15, 84, 85\} \)[/tex]
- Check each element: 39, 51, 15, 84, and 85.
- All elements are in [tex]\( A \)[/tex].
- Therefore, [tex]\( D \)[/tex] is a subset of [tex]\( A \)[/tex].
5. Set [tex]\( E = \{39, 84, 15, 85, 22, 51, 18\} \)[/tex]
- Check each element: 18 is not in [tex]\( A \)[/tex].
- Since 18 is missing from [tex]\( A \)[/tex], [tex]\( E \)[/tex] is not a subset of [tex]\( A \)[/tex].
6. Set [tex]\( H = \{85, 51, 22, 15\} \)[/tex]
- Check each element: 85, 51, 22, and 15.
- All elements are in [tex]\( A \)[/tex].
- Therefore, [tex]\( H \)[/tex] is a subset of [tex]\( A \)[/tex].
After this analysis, the sets that are subsets of [tex]\( A \)[/tex] are [tex]\( C \)[/tex], [tex]\( D \)[/tex], and [tex]\( H \)[/tex].
Let's go through each set:
1. Set [tex]\( C = \{85, 84, 22, 39, 15, 51\} \)[/tex]
- Check each element: 85, 84, 22, 39, 15, and 51.
- All elements are in [tex]\( A \)[/tex].
- Therefore, [tex]\( C \)[/tex] is a subset of [tex]\( A \)[/tex].
2. Set [tex]\( F = \{88, 51, 22, 85, 84, 39\} \)[/tex]
- Check each element: 88 is not in [tex]\( A \)[/tex].
- Since 88 is missing from [tex]\( A \)[/tex], [tex]\( F \)[/tex] is not a subset of [tex]\( A \)[/tex].
3. Set [tex]\( G = \{85, 54, 51, 39, 15\} \)[/tex]
- Check each element: 54 is not in [tex]\( A \)[/tex].
- Since 54 is missing from [tex]\( A \)[/tex], [tex]\( G \)[/tex] is not a subset of [tex]\( A \)[/tex].
4. Set [tex]\( D = \{39, 51, 15, 84, 85\} \)[/tex]
- Check each element: 39, 51, 15, 84, and 85.
- All elements are in [tex]\( A \)[/tex].
- Therefore, [tex]\( D \)[/tex] is a subset of [tex]\( A \)[/tex].
5. Set [tex]\( E = \{39, 84, 15, 85, 22, 51, 18\} \)[/tex]
- Check each element: 18 is not in [tex]\( A \)[/tex].
- Since 18 is missing from [tex]\( A \)[/tex], [tex]\( E \)[/tex] is not a subset of [tex]\( A \)[/tex].
6. Set [tex]\( H = \{85, 51, 22, 15\} \)[/tex]
- Check each element: 85, 51, 22, and 15.
- All elements are in [tex]\( A \)[/tex].
- Therefore, [tex]\( H \)[/tex] is a subset of [tex]\( A \)[/tex].
After this analysis, the sets that are subsets of [tex]\( A \)[/tex] are [tex]\( C \)[/tex], [tex]\( D \)[/tex], and [tex]\( H \)[/tex].
