Question

Let the Universal Set, S, have 85 elements. A and B are subsets of S. Set A contains 49 elements and Set B contains 51 elements. If Sets A and B have 41 elements in common, how many elements are in B but not in A?

Answer 1

The number of elements that are in B but not in A is 10.

Explanation:

we can use the formula:

n(B\A) = n(B) - n(A ∩ B)

where n(B\A) represents the number of elements in B but not in A.

Given:

S has 85 elements

A has 49 elements

B has 51 elements

A and B have 41 elements in common

Using these values in the formula, we get:

n(B\A) = n(B) - n(A ∩ B)

n(B\A) = 51 - 41

n(B\A) = 10

Therefore, there are 10 elements in B but not in A.