Question

if n(A-B) =30,n(B-A)=50 and n(A n B) =20 find n(A u B)

Answer 1

Answer:

hey dude here is your answer...

n(A-b)=30

n(b-a) =50

n(AnB)=20

n(AuB)=?

n(AuB)=n(A-B)+n(b-a) -n(AnB)

n(AuB)=n(a)+n(b)-n(AnB)

n(AuB)=30+50-20

n(AuB)=80-20

n(AuB)=60

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Answer 2

n(A ∪ B) = 100.

Given:

n(A - B) = 30, n(B - A) = 50, and n(A ∩ B) =20

To Find:

n(A ∪ B) =?

Solution:

There are two sets, A and B.

We have been given that n(A - B) = 30.

⇒ The number of elements that are present in A only = 30.

Also, n(B - A) = 50.

⇒ The number of elements that are present in B only = 50.

It is also given that

n(A ∩ B) =20

⇒ The number of elements that are common to A and B = 20.

The number of elements in the union of two sets A and B consists of elements that are present in A only, B only, and those elements that are common to both A and B. Writing this in terms of an equation, we have:

n(A ∪ B) = n(A - B) + n(B - A) + n(A ∩ B) = 30 + 50 + 20 = 100.

∴ n(A ∪ B) = 100.

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