To determine which of the given sets is a subset of [tex]\( A \)[/tex], we must check if every element of each set is also an element of [tex]\( A \)[/tex]. Let's consider each set one by one:
1. Set [tex]\( F = \{64, 27, 30, 42, 34, 19\} \)[/tex]:
- Elements of [tex]\( F \)[/tex] are [tex]\( 64, 27, 30, 42, 34, 19 \)[/tex].
- Compare each element with set [tex]\( A = \{83, 27, 68, 19, 34, 42, 30\} \)[/tex].
- [tex]\( 64 \)[/tex] is not in [tex]\( A \)[/tex], so [tex]\( F \)[/tex] cannot be a subset of [tex]\( A \)[/tex].
2. Set [tex]\( C = \{34, 27, 83, 42, 49, 19, 30, 68\} \)[/tex]:
- Elements of [tex]\( C \)[/tex] are [tex]\( 34, 27, 83, 42, 49, 19, 30, 68 \)[/tex].
- Compare each element with set [tex]\( A = \{83, 27, 68, 19, 34, 42, 30\} \)[/tex].
- [tex]\( 49 \)[/tex] is not in [tex]\( A \)[/tex], so [tex]\( C \)[/tex] cannot be a subset of [tex]\( A \)[/tex].
3. Set [tex]\( E = \{30, 83, 34, 27, 68, 42\} \)[/tex]:
- Elements of [tex]\( E \)[/tex] are [tex]\( 30, 83, 34, 27, 68, 42 \)[/tex].
- Compare each element with set [tex]\( A = \{83, 27, 68, 19, 34, 42, 30\} \)[/tex].
- All elements of [tex]\( E \)[/tex] ([tex]\( 30, 83, 34, 27, 68, 42 \)[/tex]) are in [tex]\( A \)[/tex], so [tex]\( E \)[/tex] is indeed a subset of [tex]\( A \)[/tex].
4. Set [tex]\( D = \{72, 30, 19, 27, 68, 42, 34\} \)[/tex]:
- Elements of [tex]\( D \)[/tex] are [tex]\( 72, 30, 19, 27, 68, 42, 34 \)[/tex].
- Compare each element with set [tex]\( A = \{83, 27, 68, 19, 34, 42, 30\} \)[/tex].
- [tex]\( 72 \)[/tex] is not in [tex]\( A \)[/tex], so [tex]\( D \)[/tex] cannot be a subset of [tex]\( A \)[/tex].
After comparing all given sets with [tex]\( A \)[/tex], the only set that is a subset of [tex]\( A \)[/tex] is [tex]\( E \)[/tex].
Hence, the set [tex]\( E = \{30, 83, 34, 27, 68, 42\} \)[/tex] is a subset of [tex]\( A \)[/tex].
