Question

If $A=(5,6,7,8,9),B=\{x:3<x<8\text{and}x\in W\}$ and $C=\{x:x\le 5\text{and}x\in N\}$. Find number of elements in A $\cap$ B and (A $\cap$ B) $\cap$ C.

Answer 1

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, A∩B=A∩B= { 5,6,75,6,7 }
And, (A∩B)∩C=(A∩B)∩C= { 5,6,75,6,7 }∩∩ { 1,2,3,4,51,2,3,4,5 } == { 55 }