Question

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}

Answer 1

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.