Sets Operations
If A × B = {(1,2), (1,3), (2,2), (2,3)}, then which of the following is correct?
Select the correct option:
Solution
A = {1, 2}, B = {2, 3}
- Definition of Cartesian Product: A×B is the set of all ordered pairs (a,b) where a∈A and b∈B.
- Extract Domain (Set A): Collect all unique first coordinates from the pairs.
- First elements: {1,1,2,2}→A={1,2}.
- Extract Codomain (Set B): Collect all unique second coordinates.
- Second elements: {2,3,2,3}→B={2,3}.
- Result: A={1,2} and B={2,3}.
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About This Question
- Subject
- mathematics
- Chapter
- sets, relations and functions
- Topic
- sets operations
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
A = {1, 2}, B = {2, 3}
- Definition of Cartesian Product: A×B is the set of all ordered pairs (a,b) where a∈A and b∈B.
- Extract Domain (Set A): Collect all unique first coordinates from the pairs.
- First elements: {1,1,2,2}→A={1,2}.
- Extract Codomain (Set B): Collect all unique second coordinates.
- Second elements: {2,3,2,3}→B={2,3}.
- Result: A={1,2} and B={2,3}.
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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