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CUET PG 2022 — Mathematics PYQ

CUET PG | Mathematics | 2022

Let A = {1, 2, 3} and consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (1, 3)} then R is

Choose the correct answer:

Explanation

1. Reflexivity

A relation is reflexive if every element $a \in A$ is related to itself ( $a, a \in R$ ).

For $A = \{1, 2, 3\}$ , we check for $(1, 1), (2, 2),$ and $(3, 3)$ .

Since all three are present in $R$ , the relation is Reflexive.

2. Symmetry

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

We have $(1, 2) \in R$ , but $(2, 1) \notin R$ .

Also, $(1, 3) \in R$ , but $(3, 1) \notin R$ .

Therefore, the relation is not Symmetric.

3. Transitivity

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

Let's check the pairs:

$(1, 1)$ and $(1, 2) \implies (1, 2) \in R$ (True)

$(1, 2)$ and $(2, 2) \implies (1, 2) \in R$ (True)

$(1, 1)$ and $(1, 3) \implies (1, 3) \in R$ (True)

There are no pairs $(a, b)$ and $(b, c)$ such that $(a, c)$ is missing.

Therefore, the relation is Transitive.

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