Answer :
Given:
[tex]\begin{gathered} A=\lbrace1,2,4,7\rbrace \\ B=\lbrace1,5,6,7\rbrace \\ U=\lbrace1,2,4,5,6,7\rbrace \end{gathered}[/tex]To find:
[tex](A\cap B)^{\prime}[/tex]Explanation:
Using the property,
[tex](A\cap B)^{\prime}=U-(A\cap B)[/tex]Here,
[tex]A\cap B=\lbrace1,7\rbrace[/tex]So, the property becomes,
[tex]\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}[/tex]Final answer: Option B
[tex](A\operatorname{\cap}B)^{\prime}=\lbrace2,4,5,6\rbrace[/tex]