JAMIA 2022 — Mathematics PYQ

1. Reflexive Check

A relation $R$ on set $A$ is reflexive if $\forall a\in A,(a,a)\in R$.

• $(1,1)\in R$

• $(2,2)\in R$

• $(3,3)\in R$

  Since all elements of $A=\{1,2,3\}$ are related to themselves, $R$ is reflexive.

2. Symmetric Check

A relation $R$ is symmetric if $(a,b)\in R⟹(b,a)\in R$.

• $(1,2)\in R$ but $(2,1)\notin R$

• $(2,3)\in R$ but $(3,2)\notin R$

• $(1,3)\in R$ but $(3,1)\notin R$

  Since the reverse pairs are missing, $R$ is not symmetric.

3. Transitive Check

A relation $R$ is transitive if $(a,b)\in R$ and $(b,c)\in R⟹(a,c)\in R$.

• $(1,2)\in R$ and $(2,3)\in R⟹(1,3)\in R$ (Present)

  Therefore, $R$ is transitive.

Result:

The relation is reflexive and transitive, but not symmetric.