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

Explanation

To determine whether the relation \( R \) on \( \mathbb{R} \) defined by \( R = \{(a, b) : a \leq b^3\} \) is reflexive, symmetric, or transitive, we will check each property step by step.

### Step 1: Check if the relation is Reflexive
A relation is reflexive if for every element \( a \in \mathbb{R} \), the pair \( (a, a) \) belongs to the relation \( R \).

**Check:**
For \( (a, a) \) to belong to \( R \), we need:
\[ a \leq a^3 \]
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