Class 12 Relations And Functions · Very Long Answer5 Markstypes_of_relations

Class 12 Maths · Relations And Functions · Very Long Answer #183

On R, let aRb iff a≤b³. Test reflexivity, symmetry and transitivity.

✅ Step-by-Step Solution

Final Answer: None of the three properties holds.

Reflexivity requires a≤a³ for every real a; symmetry and transitivity also require universal implications.
At a=1/3, 1/3>1/27, so aRa fails and R is not reflexive.
1R2 is true since 1≤8, but 2R1 is false since 2>1, so R is not symmetric.
10R3 and 3R2 hold because 10≤27 and 3≤8, but 10R2 fails because 10>8, so R is not transitive.
Thus R is neither reflexive nor symmetric nor transitive.

[1 mark] Reflexivity requires a≤a³ for every real a; symmetry and transitivity also require universal implications.
[1 mark] At a=1/3, 1/3>1/27, so aRa fails and R is not reflexive.
[1 mark] 1R2 is true since 1≤8, but 2R1 is false since 2>1, so R is not symmetric.
[1 mark] 10R3 and 3R2 hold because 10≤27 and 3≤8, but 10R2 fails because 10>8, so R is not transitive.
[1 mark] Thus R is neither reflexive nor symmetric nor transitive.

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