Question

If n(A∪B)=97, n(A∩B) = 23 and n(A-B)=39, then n(B) is equal to

• A. 52
• B. 55
• C. 58
• D. 62
• E. 65

Answer 1

The Correct Option is C

We are given the following information: - \( n(A \cup B) = 97 \) - \( n(A \cap B) = 23 \) - \( n(A - B) = 39 \) We need to find \( n(B) \). We know the formula for the union of two sets: \[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \] We can also express \( n(A) \) as: \[ n(A) = n(A - B) + n(A \cap B) = 39 + 23 = 62 \] Substitute this into the union formula: \[ 97 = 62 + n(B) - 23 \] Simplifying: \[ 97 = 39 + n(B) \] So: \[ n(B) = 97 - 39 = 58 \]

The correct option is (C) : \(58\)

Answer 2

We are given the following information:

• n(A∪B) = 97
• n(A∩B) = 23
• n(A-B) = 39

We want to find n(B).

We know that: n(A) = n(A-B) + n(A∩B)

So, n(A) = 39 + 23 = 62

We also know that: n(A∪B) = n(A) + n(B) - n(A∩B)

Plugging in the given values, we have: 97 = 62 + n(B) - 23

Solving for n(B): n(B) = 97 - 62 + 23 n(B) = 35 + 23 n(B) = 58

Therefore, n(B) is equal to 58.