Let's carefully analyze the relationship between the two sets given in the problem.
First, we take a look at the two sets:
- Set [tex]\( A = \{-7, 6, 7 \} \)[/tex]
- Set [tex]\( B = \{-7, -6, 6, 7 \} \)[/tex]
To determine the correct subset relationship [tex]\( \subseteq \)[/tex] or [tex]\( \nsubseteq \)[/tex], we need to check if every element in [tex]\( A \)[/tex] is also in [tex]\( B \)[/tex].
### Step-by-Step Analysis:
1. Element [tex]\(-7\)[/tex]:
- [tex]\(-7\)[/tex] is in set [tex]\( A \)[/tex].
- [tex]\(-7\)[/tex] is also in set [tex]\( B \)[/tex].
2. Element [tex]\( 6 \)[/tex]:
- [tex]\( 6 \)[/tex] is in set [tex]\( A \)[/tex].
- [tex]\( 6 \)[/tex] is also in set [tex]\( B \)[/tex].
3. Element [tex]\( 7 \)[/tex]:
- [tex]\( 7 \)[/tex] is in set [tex]\( A \)[/tex].
- [tex]\( 7 \)[/tex] is also in set [tex]\( B \)[/tex].
Since all elements of set [tex]\( A \)[/tex] are present in set [tex]\( B \)[/tex], we have that:
[tex]\[ \{-7, 6, 7 \} \subseteq \{-7, -6, 6, 7\} \][/tex]
### Checking the Notion of Non-Subset:
By definition, since set [tex]\( A \)[/tex] is indeed a subset of set [tex]\( B \)[/tex], [tex]\(\{-7, 6, 7\} \nsubseteq \{-7, -6, 6, 7\}\)[/tex] is false.
### Final Answer:
Thus, the correct insertions for the blank in the statement are as follows:
[tex]\[ \{-7, 6, 7 \} \subseteq \{-7, -6, 6, 7\} \][/tex]
[tex]\[ \{-7, 6, 7 \} \nsubseteq \{-7, -6, 6, 7\}\][/tex]
So, we fill in the blanks:
1. [tex]\[ \{-7, 6, 7 \} \subseteq \{-7, -6, 6, 7\} \][/tex]
2. [tex]\[ \{-7, 6, 7 \} \nsubseteq \{-7, -6, 6, 7\} \][/tex]
