Show that the relation R in the set R of real numbers, defined as `R={(a ,b): alt=b^2}`is neither reflexive nor symmetric nor transitive.

Explanation

To show that the relation \( R \) defined on the set of real numbers \( \mathbb{R} \) as \( R = \{(a, b) : a \leq b^2\} \) is neither reflexive, symmetric, nor transitive, we will analyze each property step by step.

### Step 1: Check for Reflexivity
A relation \( R \) is reflexive if for every element \( a \in \mathbb{R} \), the pair \( (a, a) \) is in \( R \). This means we need to check if \( a \leq a^2 \) holds for all real numbers \( a \).

- For \( a = 0.5 \):
\[
0.5 \leq (0.5)^2 = 0.25 \quad \text{(This is false)}
...