Let's examine the problem step-by-step to determine the correct symbol to insert in the blank space.
We have the element [tex]\( 10 \)[/tex] and the set [tex]\( \{7, 8, 9, 10\} \)[/tex].
1. Identify the Elements in the Set: The set given comprises the elements \{7, 8, 9, 10\}. This means that the set contains exactly these four elements: 7, 8, 9, and 10.
2. Check for Element Membership: We need to determine if the number 10 is part of the set \{7, 8, 9, 10\}. An element is considered to be in a set if it can be found within the brackets that define the set.
3. Compare the Element with Set: Look within the set to see if the number 10 is present. In this case, we find that 10 is indeed one of the elements listed in the set \{7, 8, 9, 10\}.
4. Select the Correct Symbol:
- The symbol [tex]\( \in \)[/tex] (also written as [tex]\( € \)[/tex]) means "is an element of".
- The symbol [tex]\( \notin \)[/tex] means "is not an element of".
Since the number 10 is an element of the set \{7, 8, 9, 10\}, the correct statement is:
[tex]\[ 10 \in \{7, 8, 9, 10\} \][/tex]
Thus, the blank should be filled with [tex]\( \in \)[/tex] ([tex]\(\epsilon\)[/tex]).
Therefore, the correct answer is:
A. [tex]\( \epsilon \)[/tex]
