Question 39

For a set S, we denote by S', the complement of the set S. Let X, Y, Z be Sets such that $$Y \subseteq X$$. Which of the following is always true?

Solution

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Consider the above Diagram

For option A $$X\cap Z$$ = c+e and $$Y\cap Z$$ = e. Hence option A is False

For Option B $$Y'\cap Z'$$ = a+u  and $$X'\cap Z'$$ = u. Hence option B is False

For Option C $$X\cap\left(Y\cup Z\right)$$ = c+d+e and $$Y\cup\left(X\cap Z\right)$$ = c+d+e. Hence option C is True

For option D $$X'\cap Z$$ = b and $$Y'\cap Z$$ = b+c. Hence option D is False

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