To determine which of the given sets are subsets of [tex]\( P = \{-3, -2, 2, 3, 7\} \)[/tex], we need to check if every element in each subset is also an element of [tex]\( P \)[/tex].
1. Subset [tex]\(\{2\}\)[/tex]:
- This set contains just one element, 2.
- Checking if 2 is in [tex]\( P \)[/tex]:
- Yes, [tex]\( 2 \in \{-3, -2, 2, 3, 7\} \)[/tex].
- Therefore, [tex]\(\{2\}\)[/tex] is a subset of [tex]\( P \)[/tex].
2. Subset [tex]\(\{-7\}\)[/tex]:
- This set contains just one element, -7.
- Checking if -7 is in [tex]\( P \)[/tex]:
- No, [tex]\( -7 \notin \{-3, -2, 2, 3, 7\} \)[/tex].
- Therefore, [tex]\(\{-7\}\)[/tex] is not a subset of [tex]\( P \)[/tex].
3. Subset [tex]\(\{-3, 3, 7\}\)[/tex]:
- This set contains three elements: -3, 3, and 7.
- Checking if -3, 3, and 7 are in [tex]\( P \)[/tex]:
- Yes, [tex]\( -3 \in \{-3, -2, 2, 3, 7\} \)[/tex].
- Yes, [tex]\( 3 \in \{-3, -2, 2, 3, 7\} \)[/tex].
- Yes, [tex]\( 7 \in \{-3, -2, 2, 3, 7\} \)[/tex].
- Therefore, [tex]\(\{-3, 3, 7\}\)[/tex] is a subset of [tex]\( P \)[/tex].
4. Subset [tex]\(\{3, 7\}\)[/tex]:
- This set contains two elements: 3 and 7.
- Checking if 3 and 7 are in [tex]\( P \)[/tex]:
- Yes, [tex]\( 3 \in \{-3, -2, 2, 3, 7\} \)[/tex].
- Yes, [tex]\( 7 \in \{-3, -2, 2, 3, 7\} \)[/tex].
- Therefore, [tex]\(\{3, 7\}\)[/tex] is a subset of [tex]\( P \)[/tex].
Based on this analysis:
- [tex]\(\{2\}\)[/tex] is a subset of [tex]\( P \)[/tex].
- [tex]\(\{-7\}\)[/tex] is not a subset of [tex]\( P \)[/tex].
- [tex]\(\{-3, 3, 7\}\)[/tex] is a subset of [tex]\( P \)[/tex].
- [tex]\(\{3, 7\}\)[/tex] is a subset of [tex]\( P \)[/tex].
The sets that are subsets of [tex]\( P \)[/tex] are:
[tex]\(\{2\}\)[/tex],
[tex]\(\{-3, 3, 7\}\)[/tex], and
[tex]\(\{3, 7\}\)[/tex].
