Question

If A and B are two sets containing 13 and 16 elements respectively, then find the minimum and maximum number of elements in AUB?

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Answer 1

Step-by-step explanation:

n(A)=3

n(B)=6

n(A∪B)=n(A)+n(B)−n(A∩B)

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. A and B 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