If `A` and `B` are two sets containing `3` and `6` elements respective – InterviewSolution

InterviewSolution

1.	If `A` and `B` are two sets containing `3` and `6` elements respectively, what can be the maximum number of elements in` A cup B `. Find also the minimum number of elements in `A cup B`.
Answer» We know that ` n(A cup B) =n(A) +n(B) -n(AcapB) ......(i) ` Case 1 From (i) , it is clear that `n (AcupB) ` will be maximum when ` n(A cap B) =0`. In that case, `n(A cup B) =n(A) +n(B)=(3+6)=9`. `therefore` Maximum number of elements in `(Acup B)=9` . Case 2 From (i) , it is clearf that `n(Acup B)` will be minimum when ` n(A cap B)=0`. maximum ,i.e, when `n(Acap B) =3`. In this case, ` n(Acup B) =n(A) +n(B)-n(A cap B) =(3+6-3)=6`. `therefore` minimum number of elements in `A cup B=6`.

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