Sets Operations
For any two sets A and B, the symmetric difference A △ B is defined as (A - B) ∪ (B - A). If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, then n(A △ B) equals
Select the correct option:
Solution
4
- Find Individual Differences:
- A−B (in A ONLY): {1,2}.
- B−A (in B ONLY): {5,6}.
- Apply Union: Combine the exclusive sets.
- AΔB={1,2,5,6}.
- Count: The result has 4 elements.
- Alternative Method: n(A∪B)−n(A∩B).
- Union: {1,2,3,4,5,6} (6 elements).
- Intersection: {3,4} (2 elements).
- 6−2=4.
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About This Question
- Subject
- mathematics
- Chapter
- sets, relations and functions
- Topic
- sets operations
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
4
- Find Individual Differences:
- A−B (in A ONLY): {1,2}.
- B−A (in B ONLY): {5,6}.
- Apply Union: Combine the exclusive sets.
- AΔB={1,2,5,6}.
- Count: The result has 4 elements.
- Alternative Method: n(A∪B)−n(A∩B).
- Union: {1,2,3,4,5,6} (6 elements).
- Intersection: {3,4} (2 elements).
- 6−2=4.
This medium difficulty mathematics question is from the chapter sets, relations and functions, covering the topic of sets operations. It appeared in the 2025 exam.
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