JEE Main 2024 (Online) 4th April Evening ShiftQuestion 1
Let a relation $R$ on $\mathbb{N}\times\mathbb{N}$ be defined as: $(x_1,y_1)\,R\,(x_2,y_2)$ if and only if $x_1\le x_2$ or $y_1\le y_2$.
Consider the two statements:
(I) $R$ is reflexive but not symmetric.
(II) $R$ is transitive.
Then which one of the following is true?
Sets, Relations and Function
Solution
$(a,b)R(a,b)$ always, so $R$ is reflexive; $(1,1)R(2,2)$ but not $(2,2)R(1,1)$, so it is not symmetric. $(3,1)R(1,2)$ and $(1,2)R(2,0)$ but $(3,1)$ is not related to $(2,0)$, so $R$ is not transitive. Only (I) is correct.