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Question

If $A equals open curly brackets a comma b comma blank c close curly brackets comma blank B equals left curly bracket b comma blank c comma blank d right curly bracket$ and $C equals left curly bracket a comma blank d comma blank c right curly bracket$ , then $open parentheses A minus B close parentheses cross times left parenthesis B intersection C right parenthesis$ is equal to

(a) ${(a, c), (a, d)}$
${(a, b), (c, d)}$
${(c, a), (d, a)}$
${(a, c), (a, d), (b, d)}$

The correct answer is: (a) $left curly bracket open parentheses a comma blank c close parentheses comma blank left parenthesis a comma blank d right parenthesis right curly bracket$

Given, $A equals open curly brackets a comma blank b comma blank c close curly brackets comma blank B equals left curly bracket b comma blank c comma blank d right curly bracket$ and $C equals left curly bracket a comma blank d comma blank c right curly bracket$
Now, $A minus B equals open curly brackets a comma blank b comma blank c close curly brackets minus open curly brackets b comma blank c comma blank d close curly brackets equals left curly bracket a right curly bracket$
And $B intersection C equals open curly brackets b comma blank c comma blank d close curly brackets intersection open curly brackets a comma blank d comma blank c close curly brackets equals left curly bracket c comma blank d right curly bracket$
$therefore open parentheses A minus B close parentheses cross times open parentheses B intersection C close parentheses equals left curly bracket a right curly bracket cross times left curly bracket c comma blank d$
$blank equals left curly bracket open parentheses a comma blank c close parentheses comma blank left parenthesis a comma blank d right parenthesis right curly bracket$

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