Answer :
Certainly! Let's determine which of the given sets is a subset of [tex]\( A = \{30, 32, 23, 50, 76, 80, 93\} \)[/tex].
A set [tex]\( B \)[/tex] is a subset of another set [tex]\( A \)[/tex] if every element of [tex]\( B \)[/tex] is also an element of [tex]\( A \)[/tex].
Here are the steps to check each given set:
1. Set [tex]\( C = \{23, 32, 50, 76, 30, 22, 80, 93\} \)[/tex]:
- Elements: 23, 32, 50, 76, 30, 22, 80, 93
- Check if each element of [tex]\( C \)[/tex] is in [tex]\( A \)[/tex]:
- 23, 32, 50, 76, 30, 80, and 93 are in [tex]\( A \)[/tex].
- 22 is not in [tex]\( A \)[/tex].
- Since 22 is not in [tex]\( A \)[/tex], [tex]\( C \)[/tex] is not a subset of [tex]\( A \)[/tex].
2. Set [tex]\( D = \{93, 30, 76, 83, 23, 80, 50\} \)[/tex]:
- Elements: 93, 30, 76, 83, 23, 80, 50
- Check if each element of [tex]\( D \)[/tex] is in [tex]\( A \)[/tex]:
- 93, 30, 76, 23, 80, and 50 are in [tex]\( A \)[/tex].
- 83 is not in [tex]\( A \)[/tex].
- Since 83 is not in [tex]\( A \)[/tex], [tex]\( D \)[/tex] is not a subset of [tex]\( A \)[/tex].
3. Set [tex]\( E = \{23, 32, 93, 80, 76, 50\} \)[/tex]:
- Elements: 23, 32, 93, 80, 76, 50
- Check if each element of [tex]\( E \)[/tex] is in [tex]\( A \)[/tex]:
- 23, 32, 93, 80, 76, and 50 are all in [tex]\( A \)[/tex].
- Since all elements of [tex]\( E \)[/tex] are in [tex]\( A \)[/tex], [tex]\( E \)[/tex] is a subset of [tex]\( A \)[/tex].
4. Set [tex]\( F = \{76, 32, 30, 80, 52, 93\} \)[/tex]:
- Elements: 76, 32, 30, 80, 52, 93
- Check if each element of [tex]\( F \)[/tex] is in [tex]\( A \)[/tex]:
- 76, 32, 30, 80, and 93 are in [tex]\( A \)[/tex].
- 52 is not in [tex]\( A \)[/tex].
- Since 52 is not in [tex]\( A \)[/tex], [tex]\( F \)[/tex] is not a subset of [tex]\( A \)[/tex].
Conclusion:
The set [tex]\( E = \{23, 32, 93, 80, 76, 50\} \)[/tex] is the only subset of [tex]\( A \)[/tex] among the given choices.
A set [tex]\( B \)[/tex] is a subset of another set [tex]\( A \)[/tex] if every element of [tex]\( B \)[/tex] is also an element of [tex]\( A \)[/tex].
Here are the steps to check each given set:
1. Set [tex]\( C = \{23, 32, 50, 76, 30, 22, 80, 93\} \)[/tex]:
- Elements: 23, 32, 50, 76, 30, 22, 80, 93
- Check if each element of [tex]\( C \)[/tex] is in [tex]\( A \)[/tex]:
- 23, 32, 50, 76, 30, 80, and 93 are in [tex]\( A \)[/tex].
- 22 is not in [tex]\( A \)[/tex].
- Since 22 is not in [tex]\( A \)[/tex], [tex]\( C \)[/tex] is not a subset of [tex]\( A \)[/tex].
2. Set [tex]\( D = \{93, 30, 76, 83, 23, 80, 50\} \)[/tex]:
- Elements: 93, 30, 76, 83, 23, 80, 50
- Check if each element of [tex]\( D \)[/tex] is in [tex]\( A \)[/tex]:
- 93, 30, 76, 23, 80, and 50 are in [tex]\( A \)[/tex].
- 83 is not in [tex]\( A \)[/tex].
- Since 83 is not in [tex]\( A \)[/tex], [tex]\( D \)[/tex] is not a subset of [tex]\( A \)[/tex].
3. Set [tex]\( E = \{23, 32, 93, 80, 76, 50\} \)[/tex]:
- Elements: 23, 32, 93, 80, 76, 50
- Check if each element of [tex]\( E \)[/tex] is in [tex]\( A \)[/tex]:
- 23, 32, 93, 80, 76, and 50 are all in [tex]\( A \)[/tex].
- Since all elements of [tex]\( E \)[/tex] are in [tex]\( A \)[/tex], [tex]\( E \)[/tex] is a subset of [tex]\( A \)[/tex].
4. Set [tex]\( F = \{76, 32, 30, 80, 52, 93\} \)[/tex]:
- Elements: 76, 32, 30, 80, 52, 93
- Check if each element of [tex]\( F \)[/tex] is in [tex]\( A \)[/tex]:
- 76, 32, 30, 80, and 93 are in [tex]\( A \)[/tex].
- 52 is not in [tex]\( A \)[/tex].
- Since 52 is not in [tex]\( A \)[/tex], [tex]\( F \)[/tex] is not a subset of [tex]\( A \)[/tex].
Conclusion:
The set [tex]\( E = \{23, 32, 93, 80, 76, 50\} \)[/tex] is the only subset of [tex]\( A \)[/tex] among the given choices.
