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}

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asked Oct 17, 2023 97.5k views

1 Answer

Szymon Seliga · Answer 1 · 2023-10-23T04:05:21+0000

Given that:

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

1, You need to find:

$B\cap C$

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:

$B\cap C=\lbrace1,3,7\rbrace$

2. Find:

$A\cap(B\cap C)$

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

$A\text{ }and\text{ }B\cap C$

Therefore, you get:

$A\cap(B\cap C)=\lbrace\rbrace$

Hence, the answer is: Option a.