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If n(A) = 3 and n(B) =5, then maximum nu...

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

A

`3`

B

`5`

C

`2`

D

None of these

Text Solution

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The correct Answer is:
To find the maximum number of elements in the intersection of sets A and B (denoted as A ∩ B), we can follow these steps: ### Step-by-Step Solution: 1. **Identify the number of elements in each set**: - We are given that the number of elements in set A, denoted as n(A), is 3. - We are also given that the number of elements in set B, denoted as n(B), is 5. 2. **Understand what A ∩ B means**: - The intersection of two sets A and B (A ∩ B) consists of all elements that are common to both sets. 3. **Determine the maximum possible elements in A ∩ B**: - The maximum number of elements in the intersection A ∩ B cannot exceed the number of elements in the smaller set. - Since set A has 3 elements, the maximum number of elements that can be common (i.e., in A ∩ B) is limited by the number of elements in set A. 4. **Conclusion**: - Therefore, the maximum number of elements in A ∩ B is equal to the number of elements in set A, which is 3. ### Final Answer: The maximum number of elements in A ∩ B is **3**. ---
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