Question

If A and B are disjoint sets and \(n(A)=4\) ,\(n(A∪B)=7\), then the value of \(n(B)\) is

• A. 7
• B. 4
• C. 3
• D. 11

Answer 1

The Correct Option is C

We are given the following information about two disjoint sets \( A \) and \( B \):

\( n(A) = 4 \),

\( n(A \cup B) = 7 \). 

Step 1: Understanding Disjoint Sets

Since \( A \) and \( B \) are disjoint, they have no common elements. Therefore, the formula for the number of elements in their union simplifies to:

\[ n(A \cup B) = n(A) + n(B) \]

Step 2: Substituting the Given Values

\[ 7 = 4 + n(B) \]

Solving for \( n(B) \):

\[ n(B) = 7 - 4 = 3 \]

Final Answer: \( n(B) = 3 \).

Answer 2

To find the value of \(n(B)\) when A and B are disjoint sets, we can use the formula for the union of two sets: \(n(A \cup B) = n(A) + n(B)\). 
This formula applies straightforwardly because A and B are disjoint sets, meaning they have no elements in common.

Given:

• \(n(A) = 4\)
• \(n(A \cup B) = 7\)

Substitute the known values into the formula:

\(7 = 4 + n(B)\)

To solve for \(n(B)\), subtract 4 from both sides:

\(n(B) = 7 - 4\)

\(n(B) = 3\)

Therefore, the value of \(n(B)\) is 3. 
The correct answer is 3.