Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Insert [tex]\subseteq[/tex] or [tex]\nsubseteq[/tex] in the blank so that the resulting statement is true.
[tex]\[
\begin{array}{c}
\{-7, 6, 7\} \_ \{-7, -6, 6, 7\} \\
\{-7, 6, 7\} \triangle \{-7, -6, 6, 7\}
\end{array}
\][/tex]

Sagot :

GinnyAnswer
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]
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.