Question

N(U)=100
n.(A)=20
n(A n B)=30
n(A u B)=100
n(B)=?​

Answer 1

To find the value of n(B), we can use the formula for the union of two sets:

n(A U B) = n(A) + n(B) - n(A n B)

where:

n(A U B) is the total number of elements in the union of sets A and B.

n(A) is the number of elements in set A.

n(B) is the number of elements in set B.

n(A n B) is the number of elements that are common to both sets A and B.

We are given the following information:

n(A) = 20

n(A n B) = 30

n(A U B) = 100

Let's plug in these values into the formula and solve for n(B):

100 = 20 + n(B) - 30

Add 30 to both sides:

130 = 20 + n(B)

Subtract 20 from both sides:

n(B) = 130 - 20

n(B) = 110

So, the number of elements in set B (n(B)) is 110.

Explanation: