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Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2...

Show that the relation R in the set {1, | Class 12 Mathematics Chapter Relations and Functions, Relations and Functions NCERT Solutions

Question: 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.

Answer:

Let A = {1, 2, 3}.

A relation R on A is defined as R = {(1, 2), (2, 1)}.

It is seen that (1, 1), (2, 2), (3, 3) ∉R.

∴ R is not reflexive.

Now, as (1, 2) ∈ R and (2, 1) ∈ R, then R is symmetric.

Now, (1, 2) and (2, 1) ∈ R

However,

(1, 1) ∉ R

∴ R is not transitive.

Hence, R is symmetric but neither reflexive nor transitive.

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Popular questions of class 12 Mathematics

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Welcome to the NCERT Solutions for Class 12 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 1 , Question 6: Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither....

Show that the relation R in the set {1, | Class 12 Mathematics Chapter Relations and Functions, Relations and Functions NCERT Solutions

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