Question

If n(u) = 120, n(A)=80, n(B) = 60and (ANB) = 30 then find(AUB).

Answer 1

The number of elements in the union of sets A and B, which is denoted by n(A ∪ B), is calculated to be 110 using the principle of inclusion and exclusion with the provided values. Thus, the number of elements in the union of sets A and B is 110.

Step-by-step explanation:

To find the number of elements in the union of sets A and B, designated as n(A ∪ B), we use the principle of inclusion and exclusion. This principle can be expressed with the formula:

n(A ∪ B) = n(A) + n(B) - n(A ∩ B),

where:

• n(A) is the number of elements in set A,
• n(B) is the number of elements in set B, and
• n(A ∩ B) is the number of elements in both A and B simultaneously (the intersection of A and B).

Substituting the given values into this formula:

n(A ∪ B) = 80 + 60 - 30,

which simplifies to:

n(A ∪ B) = 110.

Thus, the number of elements in the union of sets A and B is 110.