Let A, B and C be finite sets such that A∩B∩C=ϕ and each one of the sets AΔB,BΔC and CΔA has 100 elements. The number of elements in A∪B∪C is

Let n(X ) denote the number of elements in X. Thenn(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(C∩A)+n(A∩B∩C) =Σn(A)−Σn(A∩B) (sinceA∩B∩C=ϕ)AΔB=(A−B)∪(B−A)=(A∪B)−(A∩B)Therefore,n(AΔB)=n(A∪B)−n(A∩B) =n(A)+n(B)−2n(A∩B)and 300=Σn(AΔB)=Σ[n(A)+n(B)−2n(A∩B)] =2[Σn(A)−Σn(A∩B)]Therefore, n(A∪B∪C)=Σn(A)−Σn(A∩B)=3002=150