JAMIA 2024 — Mathematics PYQ

1. Reflexivity

A relation $R$ on set $A$ is reflexive if for every $a\in A$, the pair $(a,a)\in R$.

• Here, $A=\{1,2,3\}$.

• The relation contains $(1,1)$, $(2,2)$, and $(3,3)$.

• Result: $R$ is Reflexive.

2. Symmetry

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

• In this relation, we have $(1,2)\in R$, but the reverse pair $(2,1)\notin R$.

• Similarly, we have $(2,3)\in R$ but $(3,2)\notin R$.

• Result: $R$ is Not Symmetric.

3. Transitivity

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

• Let's check the pairs:

  • $(1,2)\in R$ and $(2,3)\in R⟹(1,3)\in R$ (Which is present in $R$).

  • $(1,1)\in R$ and $(1,2)\in R⟹(1,2)\in R$ (Which is present in $R$).

• Since all such combinations hold true, the condition is satisfied.

• Result: $R$ is Transitive.

Final Answer

The relation $R$ is Reflexive and Transitive but not Symmetric.