Answer :
Let's determine which of the given sets is a subset of [tex]\( A = \{39, 43, 73, 40, 96, 49, 99\} \)[/tex].
A set [tex]\( B \)[/tex] is a subset of [tex]\( A \)[/tex] if every element in [tex]\( B \)[/tex] is also an element in [tex]\( A \)[/tex].
### Set [tex]\( F = \{99, 39, 96, 49, 73, 40\} \)[/tex]
Let's check each element:
- 99 is in [tex]\( A \)[/tex]
- 39 is in [tex]\( A \)[/tex]
- 96 is in [tex]\( A \)[/tex]
- 49 is in [tex]\( A \)[/tex]
- 73 is in [tex]\( A \)[/tex]
- 40 is in [tex]\( A \)[/tex]
Since all elements of [tex]\( F \)[/tex] are in [tex]\( A \)[/tex], [tex]\( F \)[/tex] is a subset of [tex]\( A \)[/tex].
### Set [tex]\( D = \{49, 96, 40, 73, 99, 61, 43\} \)[/tex]
- 49 is in [tex]\( A \)[/tex]
- 96 is in [tex]\( A \)[/tex]
- 40 is in [tex]\( A \)[/tex]
- 73 is in [tex]\( A \)[/tex]
- 99 is in [tex]\( A \)[/tex]
- 61 is not in [tex]\( A \)[/tex]
- 43 is in [tex]\( A \)[/tex]
Since 61 is not in [tex]\( A \)[/tex], [tex]\( D \)[/tex] is not a subset of [tex]\( A \)[/tex].
### Set [tex]\( E = \{39, 49, 84, 99, 43, 40\} \)[/tex]
- 39 is in [tex]\( A \)[/tex]
- 49 is in [tex]\( A \)[/tex]
- 84 is not in [tex]\( A \)[/tex]
- 99 is in [tex]\( A \)[/tex]
- 43 is in [tex]\( A \)[/tex]
- 40 is in [tex]\( A \)[/tex]
Since 84 is not in [tex]\( A \)[/tex], [tex]\( E \)[/tex] is not a subset of [tex]\( A \)[/tex].
### Set [tex]\( C = \{73, 96, 40, 43, 49, 45, 99, 39\} \)[/tex]
- 73 is in [tex]\( A \)[/tex]
- 96 is in [tex]\( A \)[/tex]
- 40 is in [tex]\( A \)[/tex]
- 43 is in [tex]\( A \)[/tex]
- 49 is in [tex]\( A \)[/tex]
- 45 is not in [tex]\( A \)[/tex]
- 99 is in [tex]\( A \)[/tex]
- 39 is in [tex]\( A \)[/tex]
Since 45 is not in [tex]\( A \)[/tex], [tex]\( C \)[/tex] is not a subset of [tex]\( A \)[/tex].
### Conclusion
After checking all the sets, we find that only [tex]\( F = \{99, 39, 96, 49, 73, 40\} \)[/tex] is a subset 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 in [tex]\( A \)[/tex].
### Set [tex]\( F = \{99, 39, 96, 49, 73, 40\} \)[/tex]
Let's check each element:
- 99 is in [tex]\( A \)[/tex]
- 39 is in [tex]\( A \)[/tex]
- 96 is in [tex]\( A \)[/tex]
- 49 is in [tex]\( A \)[/tex]
- 73 is in [tex]\( A \)[/tex]
- 40 is in [tex]\( A \)[/tex]
Since all elements of [tex]\( F \)[/tex] are in [tex]\( A \)[/tex], [tex]\( F \)[/tex] is a subset of [tex]\( A \)[/tex].
### Set [tex]\( D = \{49, 96, 40, 73, 99, 61, 43\} \)[/tex]
- 49 is in [tex]\( A \)[/tex]
- 96 is in [tex]\( A \)[/tex]
- 40 is in [tex]\( A \)[/tex]
- 73 is in [tex]\( A \)[/tex]
- 99 is in [tex]\( A \)[/tex]
- 61 is not in [tex]\( A \)[/tex]
- 43 is in [tex]\( A \)[/tex]
Since 61 is not in [tex]\( A \)[/tex], [tex]\( D \)[/tex] is not a subset of [tex]\( A \)[/tex].
### Set [tex]\( E = \{39, 49, 84, 99, 43, 40\} \)[/tex]
- 39 is in [tex]\( A \)[/tex]
- 49 is in [tex]\( A \)[/tex]
- 84 is not in [tex]\( A \)[/tex]
- 99 is in [tex]\( A \)[/tex]
- 43 is in [tex]\( A \)[/tex]
- 40 is in [tex]\( A \)[/tex]
Since 84 is not in [tex]\( A \)[/tex], [tex]\( E \)[/tex] is not a subset of [tex]\( A \)[/tex].
### Set [tex]\( C = \{73, 96, 40, 43, 49, 45, 99, 39\} \)[/tex]
- 73 is in [tex]\( A \)[/tex]
- 96 is in [tex]\( A \)[/tex]
- 40 is in [tex]\( A \)[/tex]
- 43 is in [tex]\( A \)[/tex]
- 49 is in [tex]\( A \)[/tex]
- 45 is not in [tex]\( A \)[/tex]
- 99 is in [tex]\( A \)[/tex]
- 39 is in [tex]\( A \)[/tex]
Since 45 is not in [tex]\( A \)[/tex], [tex]\( C \)[/tex] is not a subset of [tex]\( A \)[/tex].
### Conclusion
After checking all the sets, we find that only [tex]\( F = \{99, 39, 96, 49, 73, 40\} \)[/tex] is a subset of [tex]\( A \)[/tex].
