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Sets Practice Test 1

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Question : 5 of 33

Marks: +1, -0

If A {1, 2, 3, 4}, B = {2, 4, 6, 7} andC = {2, 7, 8, 9} and (∪) is the set of {1, 2, 3,4, 6, 7, 8, 9}, then (A ∩ (B ∪ C)′)′ is:

{6, 7, 8, 9}
{1, 2, 8, 9}
{4, 6, 7, 9}
{3, 7, 8, 9}
None of the above

Solution: 👈: Video Solution

Concept:

Apply De Morgan's law and set operations with universal set

U

.

Explanation:

Given

U=\{1,2,3,4,6,7,8,9\}

,

A=\{1,2,3,4\}

,

B=\{2,4,6,7\}

,

C=\{2,7,8,9\}

.

First,

B\cup C=\{2,4,6,7,8,9\}

.

Then

(B\cup C)'=U\setminus(B\cup C)=\{1,3\}

.

Now

A\cap(B\cup C)'=\{1,2,3,4\}\cap\{1,3\}=\{1,3\}

.

Finally,

(A\cap(B\cup C)')'=U\setminus\{1,3\}=\{2,4,6,7,8,9\}

.

This result is not present in options A–D.

Answer:

\{2,4,6,7,8,9\}

, hence the correct option is None of the above.

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