Question

Check whether the relation R in R defined by $R = {(a, b) : a \leq b^3}$ is reflexive,symmetric or transitive.

Answer 1

Here is your answer .I hope it will help you.

Answer 2

$\huge\mathbb\fcolorbox{Green}{violet}{♡ᎪղՏωᎬя᭄}$

$R = \{(a, b): a \leq b ^3 \} \\ It is observed that (\dfrac{1}{2},\dfrac{1}{2}) \notin R,since, \dfrac{1}{2}>(\dfrac{1}{2})^3 \\ \therefore R is not reflexive. \\ Now, (1, 2) \in R (as 1 < 2^ 3 = 8 ) \\ But, (2, 1) \notin R (as 2 ^3 > 1 ) \\ \therefore R is not symmetric. \\ We have (3,\dfrac{3}{2}),(\dfrac{3}{2},\dfrac{6}{5})$$\in R, since 3<(\dfrac{3}{2})^2 and \dfrac{3}{2}<(\dfrac{6}{5})^3 \\ But (3,\dfrac{6}{5}) \notin R as 3> (\dfrac{6}{5})^3 \\ \therefore R is not$