Question

A Venn diagram is shown below:What are the elements of (A ∩ B) ' ? A. {1, 7}B. {2, 4, 5, 6}C. {1, 2, 4, 7}D. {1, 2 ,4, 5, 6, 7}

Answer 1

Given:

`\begin{gathered} A=\lbrace1,2,4,7\rbrace \\ B=\lbrace1,5,6,7\rbrace \\ U=\lbrace1,2,4,5,6,7\rbrace \end{gathered}`

To find:

`(A\cap B)^(\prime)`

Step-by-step explanation:

Using the property,

`(A\cap B)^(\prime)=U-(A\cap B)`

Here,

`A\cap B=\lbrace1,7\rbrace`

So, the property becomes,

`\begin{gathered} (A\cap B)^(\prime)=\lbrace1,2,4,5,6,7\rbrace-\lbrace1,7\rbrace \\ (A\cap B)^(\prime)=\lbrace2,4,5,6\rbrace \end{gathered}`

Final answer: Option B