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Question

If A is the set of the divisors of the number 15, B is the set of prime numbers smaller than 10 and C is the set of even numbers smaller than 9, then (AC)B is?


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Solution

Find the required set by writing list form of sets:

It is given, that

A is the set of the divisors of the number 15, that is

A={1,3,5,15}

B is the set of prime numbers smaller than 10, that is

B={2,3,5,7}

C is the set of even numbers smaller than 9, that is

C={2,4,6,8}

Now,

(AC)={1,3,5,15}{2,4,6,8}(AC)={1,2,3,4,5,6,8,15}(AC)B={1,2,3,4,5,6,8,15}{2,3,5,7}(AC)B={2,3,5}

Hence, (AC)B={2,3,5}


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