Question

If n(A) = 25, n(B) = 40,
n(A union B) = 50 and n(B') =25,
find n(U)
Formula => n(U) = n(A) + n(A')
=> n(A') = n(U) - n(A)​

Answer 1

Answer:

Being sure of whats what can help you figure this solution easily...:)

n(AUB) means the the number of elements in both A & B. And that includes the ones in common too.

n(A∩B) means the ones that in common.

n(A-B) refers to the elements that belong to A alone. That means the elements in A excluding the common elements.

n(B) is the number of elements that belong to B and that includes the common ones too.

Now coming to your question.

The total number of elements that can fit in both the sets is 36.

While the number of common elements is 16.

And also given that n(A-B)=15.

Now according to the definitions above....n(A) should include the ones that belong exclusively to A alone and also the ones in common.

So,

n(A)=n(A-B)+n(A∩B)

=15+16

=31

Therefore, n(A) is 31.

Now when n(AUB) is 36 and n(A) is 31, it is clear that the elements exclusive to B alone is 5, i.e.36-31.

Now n(B)=n(A∩B)+n(B-A)

Therefore, n(B) is 16+5 = 21.

n(B)=21.

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