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Question

Universal set, $U equals open curly brackets x colon x to the power of 5 minus 6 x to the power of 4 plus 11 x cubed minus 6 x squared equals 0 close curly brackets$ and $A equals open curly brackets x colon x squared minus 5 x plus 6 equals 0 close curly brackets B equals open curly brackets x colon x squared minus 3 x plus 2 equals 0 close$ Then, $left parenthesis A intersection B right parenthesis to the power of straight prime$ is equal to

${1, 3}$
${1, 2, 3}$
${0, 1, 3}$
${0, 1, 2, 3}$

The correct answer is: $left curly bracket 0 comma 1 comma 3 right curly bracket$

$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell U equals open curly brackets x colon x to the power of 5 plus 6 x to the power of 4 plus 11 x cubed minus 6 x squared equals 0 close curly brackets equals left curly bracket 0 comma 1 comma 2 comma 3 right curly bracket end cell row cell A equals open curly brackets x colon x squared minus 5 x plus 6 equals 0 close curly brackets equals left curly bracket 2 comma 3 right curly bracket end cell row cell text And end text B equals open curly brackets x colon x squared minus 3 x plus 2 equals 0 close curly brackets equals left curly bracket 2 comma 1 right curly bracket end cell row cell therefore left parenthesis A intersection B right parenthesis to the power of straight prime equals U minus left parenthesis A intersection B right parenthesis end cell row cell equals left curly bracket 0 comma 1 comma 2 comma 3 right curly bracket minus left curly bracket 2 right curly bracket equals left curly bracket 0 comma 1 comma 3 right curly bracket end cell end table$

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