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Q)

if A and B be two sets containing 3 and 6 elements respectively what can be

if A and B be two sets containing 3 and 6 elements respectively what can be the minimum number of elements in A U B? and the maximum number of elements in A U B ?

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A)
n(A)=3n(A)=3

n(B)=6n(B)=6

n(A∪B)=n(A)+n(B)−n(A∩B)n

Now we have already given n(A)=3 and n(B)=6

So n(A∪B) can be minimum when n(A∩B)) is maximum or these two sets have maximum overlapping or in other words maximum elements in common. AA and BB can have atmost 3 elements common.

Then minimum no. of elements of A∪B can be achieved only when A⊂B . Note here it is proper subset symbol.

So, min(n(A∪B))=n(A)+n(B)−max(n(A∩B))=6+3−3=6

Now max value can be achieved when n(A∩B) is minimum or n(A∩B)=0

max(n(A∪B))=n(A)+n(B)−min(n(A∩B))=6+3−0=9
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