Show that the relation R in R defined as R = {(a, b): a ≤ b} is reflexive and transitive, but not symmetric

Solution:

R = {(a, b) : a ≤ b}

(a, a) ∈ R

Therefore,

R is reflexive.

(2, 4) ∈ R (as 2 < 4)

(4, 2) ∉ R (as 4>2)

Therefore,

R is not symmetric.

(a, b), (b, c) ∈ R a ≤ b and b ≤ c

⇒ a ≤ c

⇒ (a, c) ∈ R

Therefore,

R is transitive.

R is reflexive and transitive but not symmetric

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NCERT Solutions for Class 12 Maths - Chapter 1 Exercise 1.1 Question 4

Show that the relation R in R defined as R = {(a, b): a ≤ b} is reflexive and transitive, but not symmetric.

Summary:

Hence we have shown that  the relation R in R defined as R = {(a, b): a ≤ b} is reflexive and transitive, but not symmetric.