Answer :
To determine which sets are subsets of [tex]\( A = \{99, 89, 66, 10, 81, 72\} \)[/tex], let's evaluate each of the given sets one by one.
A set [tex]\( B \)[/tex] is a subset of [tex]\( A \)[/tex] if every element in [tex]\( B \)[/tex] is also an element of [tex]\( A \)[/tex].
Let's check each set:
1. Set [tex]\( D = \{10, 81, 66, 89, 72, 99\} \)[/tex]:
- This set contains elements: 10, 81, 66, 89, 72, 99.
- All these elements are present in set [tex]\( A \)[/tex].
- Therefore, [tex]\( D \)[/tex] is a subset of [tex]\( A \)[/tex].
2. Set [tex]\( G = \{99, 72, 89, 66, 81\} \)[/tex]:
- This set contains elements: 99, 72, 89, 66, 81.
- All these elements are present in set [tex]\( A \)[/tex].
- Therefore, [tex]\( G \)[/tex] is a subset of [tex]\( A \)[/tex].
3. Set [tex]\( F = \{81, 59, 10, 99, 89\} \)[/tex]:
- This set contains elements: 81, 59, 10, 99, 89.
- The element 59 is not present in set [tex]\( A \)[/tex].
- Therefore, [tex]\( F \)[/tex] is not a subset of [tex]\( A \)[/tex].
4. Set [tex]\( E = \{87, 72, 66, 89, 81, 99\} \)[/tex]:
- This set contains elements: 87, 72, 66, 89, 81, 99.
- The element 87 is not present in set [tex]\( A \)[/tex].
- Therefore, [tex]\( E \)[/tex] is not a subset of [tex]\( A \)[/tex].
5. Set [tex]\( C = \{81, 11, 10, 72, 66, 89, 99\} \)[/tex]:
- This set contains elements: 81, 11, 10, 72, 66, 89, 99.
- The element 11 is not present in set [tex]\( A \)[/tex].
- Therefore, [tex]\( C \)[/tex] is not a subset of [tex]\( A \)[/tex].
6. Set [tex]\( H = \{66, 99, 89, 10\} \)[/tex]:
- This set contains elements: 66, 99, 89, 10.
- All these elements are present in set [tex]\( A \)[/tex].
- Therefore, [tex]\( H \)[/tex] is a subset of [tex]\( A \)[/tex].
In conclusion, the sets [tex]\( D \)[/tex], [tex]\( G \)[/tex], and [tex]\( H \)[/tex] are subsets of [tex]\( A \)[/tex].
A set [tex]\( B \)[/tex] is a subset of [tex]\( A \)[/tex] if every element in [tex]\( B \)[/tex] is also an element of [tex]\( A \)[/tex].
Let's check each set:
1. Set [tex]\( D = \{10, 81, 66, 89, 72, 99\} \)[/tex]:
- This set contains elements: 10, 81, 66, 89, 72, 99.
- All these elements are present in set [tex]\( A \)[/tex].
- Therefore, [tex]\( D \)[/tex] is a subset of [tex]\( A \)[/tex].
2. Set [tex]\( G = \{99, 72, 89, 66, 81\} \)[/tex]:
- This set contains elements: 99, 72, 89, 66, 81.
- All these elements are present in set [tex]\( A \)[/tex].
- Therefore, [tex]\( G \)[/tex] is a subset of [tex]\( A \)[/tex].
3. Set [tex]\( F = \{81, 59, 10, 99, 89\} \)[/tex]:
- This set contains elements: 81, 59, 10, 99, 89.
- The element 59 is not present in set [tex]\( A \)[/tex].
- Therefore, [tex]\( F \)[/tex] is not a subset of [tex]\( A \)[/tex].
4. Set [tex]\( E = \{87, 72, 66, 89, 81, 99\} \)[/tex]:
- This set contains elements: 87, 72, 66, 89, 81, 99.
- The element 87 is not present in set [tex]\( A \)[/tex].
- Therefore, [tex]\( E \)[/tex] is not a subset of [tex]\( A \)[/tex].
5. Set [tex]\( C = \{81, 11, 10, 72, 66, 89, 99\} \)[/tex]:
- This set contains elements: 81, 11, 10, 72, 66, 89, 99.
- The element 11 is not present in set [tex]\( A \)[/tex].
- Therefore, [tex]\( C \)[/tex] is not a subset of [tex]\( A \)[/tex].
6. Set [tex]\( H = \{66, 99, 89, 10\} \)[/tex]:
- This set contains elements: 66, 99, 89, 10.
- All these elements are present in set [tex]\( A \)[/tex].
- Therefore, [tex]\( H \)[/tex] is a subset of [tex]\( A \)[/tex].
In conclusion, the sets [tex]\( D \)[/tex], [tex]\( G \)[/tex], and [tex]\( H \)[/tex] are subsets of [tex]\( A \)[/tex].
