If n A 71 n B 53 and n A B 27 what is n A U B?

To solve the problem regarding the union of two sets, we first need to understand the notation and what each term represents. In set theory, n(A) refers to the number of elements in set A, n(B) refers to the number of elements in set B, and n(A ∩ B) refers to the number of elements that are common to both sets A and B. The union of two sets, denoted as n(A ∪ B), represents the total number of unique elements in both sets combined.

Given the values:

• n(A) = 71
• n(B) = 53
• n(A ∩ B) = 27

To find the union of sets A and B, we can use the formula:

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

Now, substituting the values:

• n(A ∪ B) = 71 + 53 - 27

Calculating this gives:

• n(A ∪ B) = 124 - 27
• n(A ∪ B) = 97

Therefore, the total number of unique elements in the union of sets A and B is 97.