CBSE Class 12 Mathematics 2026 Main Paper 65(B) · Q364 Marksrelation_properties
CBSE Class 12 Mathematics 2026 Main Paper 65(B) · Question 36 (Relations And Functions)
Two friends play a dice game with outcome set B={1,2,3,4,5,6}. Define R on B by xRy when y is divisible by x.
Part (1) 1 Marks
List R.
Answer: {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,2),(2,4),(2,6),(3,3),(3,6),(4,4),(5,5),(6,6)}.
- For each x list the multiples of x within B.
- Collect the resulting fourteen ordered pairs.
Part (2) 1 Marks
Is R reflexive?
Answer: Yes.
- Every positive integer divides itself.
- Thus each (x,x) is in R.
Part (3) 2 Marks
Test symmetry and transitivity.
Answer: Not symmetric, but transitive.
- Since 1 divides 2 but 2 does not divide 1, symmetry fails.
- If x divides y and y divides z then z is a multiple of x.
- Thus the relation is transitive.
Part (4) 2 Marks
Test R₁={(x,y):x=2y} for reflexivity, symmetry and transitivity.
Answer: None of the three.
- R₁={(2,1),(4,2),(6,3)}, which lacks all diagonal pairs.
- It lacks the reverse of (2,1), so is not symmetric.
- The pairs (4,2) and (2,1) are present but (4,1) is missing, so transitivity fails.