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Question

If A={x:x=n, nN, 5n<9},

B={3,4,5,6} and

C={x=2n, nN, n<5}, then

B(AC)= ___.


A

{3,4,5,6,7}

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B

{6,8}

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C

{3,4,5,6}

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D

{3,4,5,6,8}

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Solution

The correct option is D

{3,4,5,6,8}


Writing the given sets in roster form, we get

A={5,6,7,8}

B={3,4,5,6}

C={2,4,6,8}.

Using distributive property, we have B(AC)=(BA)(BC).

={3,4,5,6,7,8}{2,3,4,5,6,8}

={3,4,5,6,8}


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