To find the possible values of [tex]\(x\)[/tex] that belong to the set [tex]\(E\)[/tex] but do not belong to the union of sets [tex]\(A\)[/tex] and [tex]\(B\)[/tex], follow these steps:
1. Identify Sets and Operations:
- Given set [tex]\(E = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}\)[/tex].
- Given set [tex]\(A = \{2, 3, 5, 7\}\)[/tex].
- Given set [tex]\(B = \{4, 6, 8, 10\}\)[/tex].
2. Compute the Union of Sets [tex]\(A\)[/tex] and [tex]\(B\)[/tex]:
[tex]\[
A \cup B = \{2, 3, 4, 5, 6, 7, 8, 10\}
\][/tex]
By combining all elements from [tex]\(A\)[/tex] and [tex]\(B\)[/tex], we get the set [tex]\(\{2, 3, 4, 5, 6, 7, 8, 10\}\)[/tex].
3. Determine Elements in [tex]\(E\)[/tex] but Not in [tex]\(A \cup B\)[/tex]:
We need to find [tex]\(x \in E\)[/tex] such that [tex]\(x \notin A \cup B\)[/tex]. This means finding elements that are in [tex]\(E\)[/tex] but not in the union set [tex]\(A \cup B\)[/tex].
[tex]\[
E - (A \cup B) = \{1, 9\}
\][/tex]
4. Conclusion:
The elements of set [tex]\(E\)[/tex] that are not in the union of sets [tex]\(A\)[/tex] and [tex]\(B\)[/tex] are [tex]\(1\)[/tex] and [tex]\(9\)[/tex].
Thus, the two possible values of [tex]\(x\)[/tex] are:
[tex]\[
\boxed{1 \text{ and } 9}
\][/tex]
