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**NCERT mathematics class 12 chapter Relations and Functions Exercise 1.1 Problem 6 Solution**. Solutions for other problems are available at Exercise 1.1 SolutionsExercise 1.1 Problem 6 Solution

6. Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

To Check whether R is Reflexive: The relation R in the set A is reflexive if (a, a) ∈ R, for every a ∈ A.

We have, 1 ∈ A but (1, 1) ∉ R

∴ R is not Reflexive

To Check whether R is Symmetric: The relation R in the set A is symmetric if (a_1, a_2) ∈ R implies that (a_2, a_1) ∈ R, for all a_1, a_2 ∈ A

We see that both (1, 2) ∈ R and (2, 1) ∈ R

⇒ R is symmetric.

To Check whether R is Transitive: The relation R in the set A is transitive if (a_1, a_2) ∈ R and (a_2, a_3) ∈ R implies that (a_1, a_3) ∈ R, for all a_1, a_2, a_3 ∈ A

We see that (1, 2) ∈ R, (2, 1) ∈ R. But (1, 1) ∉ R

∴ R is not Transitive

∴ R is symmetric but neither reflexive nor transitive.