Q5 of 107 Page 5

Check whether the relation R in R defined by R = {(a, b) : a ≤ b3} is reflexive, symmetric or transitive.

It is given that R = {(a, b) : a ≤ b3}

Now, It can observed that as


Therefore, R is not reflexive.


Now, (1,3) ϵ R(as 1 < 33 = 27)


But, (3,1) ∉ R(as 33 > 1)


Therefore, R is not symmetric.


Now, if we have



Therefore, R is not transitive.


Therefore, R is neither reflexive, nor symmetric, nor transitive.


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