Question

Let A and B be two finite sets such that n(A – B) = 30, n (A U B) = 180, n(A ∩ B) = 60, find n(B).

Answer 1

here, n(A-B)=30, n(AUB)=180, n(AnB)=60

so, n(A)=n(A-B)+n(AnB)

=30+60=90

n(B)=n(AUB)+n(AnB)-n(A)=150

so, n(B)=150..

hope it helps you.

Answer 2

Answer: The value of $n(B)$ is 150.

Step-by-step explanation:

Given: A and B be two finite sets such that n(A – B) = 30, n (A U B) = 180, n(A ∩ B) = 60.

To find:We have to find the value of $n(B)$.

Step 1: Since A and B are finite sets such that

             $n(A-B) = 30,$$n(A$∪$B) = 180$ and $(A$∩$B) = 60$

Step 2:As we know that,

            $n(B) = n(A$∪$B) - n(A-B)$

Step 3:Substituting the values we get,

⇒             $n(B) = 180 - 30$

⇒             $n(B) = 150$

∴ The value of $n(B)$ is 150.

Union of Sets:

If two sets are given as A and B, A∪B (read as A union B) is the set of distinct elements that belong to set A and set B or both. The number of elements in A ∪ B is given by n(A∪B) = n(A) + n(B) − n(A∩B). Let us understand with an example: If A = {a, b, c, d} and B = {d, e, f, g}, then the union of A and B is given by A ∪ B = {a, b, c, d, e, f, g}.

Intersection of Sets:

For two given sets A and B, A∩B (read as A intersection B) is the set of common elements that belong to set A and B. The number of elements in A∩B is given by n(A∩B) = n(A)+n(B)−n(A∪B). Let us consider an example: If A = {a, b, c, d} and B = {c, d, e, f}, then the intersection of A and B is given by A ∩ B = {c, d}.

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