Relations
Let R be a relation from set A = {2, 3, 4, 5} to set B = {1, 4, 5} defined by R = {(x, y) : x divides y}. The number of elements in R is
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About This Question
- Subject
- mathematics
- Chapter
- sets, relations and functions
- Topic
- relations
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
3
- Analyze Pair Combinations: Test each x∈A against each y∈B.
- Check Divisibility (y/x must be integer):
- From x=2: 2∣1 (No), 2∣4 (Yes), 2∣5 (No).
- From x=3: 3∣1 (No), 3∣4 (No), 3∣5 (No).
- From x=4: 4∣1 (No), 4∣4 (Yes), 4∣5 (No).
- From x=5: 5∣1 (No), 5∣4 (No), 5∣5 (Yes).
- Resulting Set: R={(2,4),(4,4),(5,5)}.
- Count: There are 3 elements.
This medium difficulty mathematics question is from the chapter sets, relations and functions, covering the topic of relations. It appeared in the 2025 exam.
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