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Use the given sets to find [tex]\((A \cap B) \cap C\)[/tex].

[tex]\[
A=\{1,2,3,4,5,6,7,8\} \\
B=\{5,7,9,11,13,15\} \\
C=\{2,4,5,7,10,12,14\}
\][/tex]


Sagot :

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]