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Question

If A=(5,6,7,8,9),B={x:3<x<8 and xW} and C={x:x5 and xN}. Find number of elements in A B and (A B) C.

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Solution

From the given sets, we have
A=(5,6,7,8,9)A=(5,6,7,8,9)
BB == { 4,5,6,74,5,6,7 } as xx is greater than 33, but less than 88
And CC == { 1,2,3,4,51,2,3,4,5 } as xx is a natural number less than equal to 55.
Intersection of two sets has the elements common in both the sets.
So, AB=A∩B= { 5,6,75,6,7 }
And, (AB)C=(A∩B)∩C= { 5,6,75,6,7 } { 1,2,3,4,51,2,3,4,5 } == { 55 }

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