Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b) : b = a + 1} is reflexive, symmetric or transitive

Solution:

A = {1, 2, 3, 4, 5, 6}

R = {(a, b) : b = a + 1}

R = {(1, 2), (2, 3), (3, 4), (4, 5), (5, 6)}

(a, a) ∉ R, a ∈ A

(1, 1), (2, 2), (3, 3), (4, 4), (5, 5) ∉ R

Therefore,

R is not reflexive.

(1, 2) ∈ R, but (2, 1) ∉ R

Therefore,

R is not symmetric.

(1, 2), (2, 3) ∈ R

(1, 3) ∉ R

Therefore,

R is not transitive.

R is neither reflexive nor symmetric nor transitive

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NCERT Solutions for Class 12 Maths - Chapter 1 Exercise 1.1 Question 3

Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b) : b = a + 1} is reflexive, symmetric or transitive.

Summary:

The relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b) : b = a + 1} is neither reflexive nor symmetric nor transitive. A relation that shows all the three given properties are called an equivalence relation