If `n(A) = 3 and n(B) =5`, then maximum number of elements in `A cap B` is :

Options

A. `3`
B. `5`
C. `2`
D. None of these

Answer

To find the maximum number of elements in the intersection of sets A and B, we can follow these steps:

### Step 1: Understand the definitions
- Let \( n(A) \) be the number of elements in set A.
- Let \( n(B) \) be the number of elements in set B.
- The intersection of sets A and B, denoted as \( A \cap B \), is the set of elements that are common to both A and B.

### Step 2: Identify the given values
- We are given that \( n(A) = 3 \) (set A has 3 elements) and \( n(B) = 5 \) (set B has 5 elements).

### Step 3: Determine the maximum possible intersection
- The maximum number of elements in the intersection \( A \cap B \) occurs when all elements of the smaller set (set A) are also in the larger set (set B).
- Since \( n(A) = 3 \), the maximum number of elements that can be in \( A \cap B \) is limited by the number of elements in A.

### Step 4: Conclusion
- Therefore, the maximum number of elements in \( A \cap B \) is \( n(A) = 3 \).

Thus, the answer is:
\[ \text{Maximum number of elements in } A \cap B = 3 \]