Answer:
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: