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Question

U={x:x is a natural number & x10}
A={a:a is an even number & a10}
B={b:b is a prime number & b9}

Then, AcBc is


A

{2,4,6,8}

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B

{3,5,7}

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C

{1,9,10}

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D

{2,3,5,7}

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Solution

The correct option is C

{1,9,10}


U={1,2,3,4,5,6,7,8,9,10}

A={2,4,6,8}

B={2,3,5,7}

Ac=UA All the elements in U which does not belong to A

={1,3,5,7,9,10}

Bc=UB Elements which belongs to U and does not belong to B

={1,4,6,8,9,10}

AcBc={1,9,10}

Alternative solution :
Using De Morgan's Law

AcBc=(AB)c
AB={2,3,4,5,6,7,8}
(AB)c={1,9,10}


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