To solve the problem [tex]\( (A \cap B) \cap C \)[/tex], we will follow a step-by-step approach:
1. Identify the sets:
[tex]\[
A = \{1, 2, 3, 4, 5, 6, 7, 8\}
\][/tex]
[tex]\[
B = \{5, 7, 9, 11, 13, 15\}
\][/tex]
[tex]\[
C = \{2, 4, 5, 7, 10, 12, 14\}
\][/tex]
2. Find the intersection of sets [tex]\(A\)[/tex] and [tex]\(B\)[/tex]:
[tex]\[
A \cap B = \{ \text{elements that are in both } A \text{ and } B \}
\][/tex]
Looking at the sets [tex]\(A\)[/tex] and [tex]\(B\)[/tex], we see that the common elements are [tex]\(5\)[/tex] and [tex]\(7\)[/tex]. Therefore,
[tex]\[
A \cap B = \{5, 7\}
\][/tex]
3. Find the intersection of [tex]\((A \cap B)\)[/tex] and [tex]\(C\)[/tex]:
[tex]\[
(A \cap B) \cap C = \{ \text{elements that are in both } (A \cap B) \text{ and } C \}
\][/tex]
Now, using [tex]\(A \cap B = \{5, 7\}\)[/tex] and [tex]\(C = \{2, 4, 5, 7, 10, 12, 14\}\)[/tex], we identify the common elements. Both [tex]\(5\)[/tex] and [tex]\(7\)[/tex] are present in set [tex]\(C\)[/tex]. Thus,
[tex]\[
(A \cap B) \cap C = \{5, 7\}
\][/tex]
Therefore, the result of [tex]\( (A \cap B) \cap C \)[/tex] is:
[tex]\[
\{5, 7\}
\][/tex]
