Question

Use the union rule to answer the question.
if n(AnB)=7, n(AuB)=5, and n(A)=34, what is n(B)

Answer 1

Question 19 n(A ∪ B) : B) 17

Question 20 n(A) : B) 34

Question 19:

We are given that n(A) = 7, n(B) = 15, and n(A ∩ B) = 5. We are asked to find n(A ∪ B).

We can use the union rule to solve for n(A ∪ B).

The union rule states that the number of elements in the union of two sets A and B is equal to the sum of the number of elements in A and the number of elements in B, minus the number of elements that are in both sets (A ∩ B).

Therefore, n(A ∪ B) = n(A) + n(B) - n(A ∩ B).

Substituting the given values, we get:

n(A ∪ B) = 7 + 15 - 5

n(A ∪ B) = 17

Therefore, the answer to question 19 is B) 17.

Question 20:

We are given that n(B) = 36, n(A ∩ B) = 7, and n(A ∪ B) = 63. We are asked to find n(A).

We can use the same approach as in question 19. However, we need to be careful because the question asks for n(A), not n(A ∪ B).

Using the union rule, we get:

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

Substituting the given values, we get:

63 = n(A) + 36 - 7

63 = n(A) + 29

n(A) = 63 - 29

n(A) = 34

Therefore, the answer to question 20 is B) 34.