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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
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.
Solution:
A = {1, 2, 3}
R = {(1, 2), (2, 1)}
(1, 1), (2, 2), (3, 3) ∉ R [ ∉ represents does not belong to ]
Therefore,
R is not reflexive.
(1, 2) ∈ R and (2, 1) ∈ R
Therefore,
R is symmetric.
(1, 2) ∈ R and (2, 1) ∈ R
(1, 1) ∈ R
Therefore,
R is not transitive.
R is symmetric but neither reflexive nor transitive
NCERT Solutions for Class 12 Maths - Chapter 1 Exercise 1.1 Question 6
Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.
Summary:
The relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive
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