JEE Main 2024 — Sets And Relations Question with Solution

$$\begin{array}{rl}& \left(x_1,y_1\right)R\left(x_2,y_2\right)\\ & \text{ If }{x}_1\le x_2\text{ or }{y}_1\le y_2\end{array}$$

For reflexive;

$$\begin{array}{rl}& \left(x_1,y_1\right)R\left(x_1,y_1\right)\\ & \Rightarrow x_1\le x_1\text{ or }{y}_1\le y_1\end{array}$$

So, $$R$$ is reflexive

For symmetric

When $$\left(x_1,y_1\right)R\left(x_2,y_2\right)$$

$$\Rightarrow x_1\le x_2\text{ or }{y}_1\le y_2$$

For $$\left(x_2,y_2\right)R\left(x_1,y_1\right)$$

$$\Rightarrow x_2\le x_1\text{ or }{y}_2\le y_1$$

Not true for $$(1,2)$$ and $$(3,4)$$

For transitive

Take pairs as $$(3,9),(4,6),(2,7)$$

$$(3,9)R(4,6)$$

as $$4\ge 3$$

$$(4,6)R(2,7)$$

As $$7\ge 6$$

But $$(3,9)R(2,7)$$

As neither $$2\ge 3$$ nor $$7\ge 9$$

So not transitive