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Let U = {1, 2, 3, 4, 5, 6, 7}, A = {2, 4, 6}, B = {1, 2, 3, 5, 7}, and C = {1, 3, 6, 7}.Find A ∩ (B ∩ C)Question 46 options:a) { }b) {2}c) {1}d) {3}

Respuesta :

Given that:

[tex]U=\lbrace1,2,3,4,5,6,7\rbrace[/tex][tex]\begin{gathered} A=\lbrace2,4,6\rbrace \\ B=\lbrace1,2,3,5,7\rbrace \\ C=\lbrace1,3,6,7\rbrace \end{gathered}[/tex]

1, You need to find:

[tex]B\cap C[/tex]

In order to find the intersection of sets B and C, you need to identify the numbers both sets have in common. Then, you get:

[tex]B\cap C=\lbrace1,3,7\rbrace[/tex]

2. Find:

[tex]A\cap(B\cap C)[/tex]

You need to identify the numbers that these sets have in common:

[tex]A\text{ }and\text{ }B\cap C[/tex]

Therefore, you get:

[tex]A\cap(B\cap C)=\lbrace\rbrace[/tex]

Hence, the answer is: Option a.

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