Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Determinants

Question:

Relation R on Real Numbers is defined as $R=\{(a, b): a \leq b\}$. The relation is :

Options:

Reflexive and Symmetric but not Transitive

Symmetric and Transitive but not Reflexive

Reflexive and Transitive but not Symmetric

Equivalence relation

Correct Answer:

Reflexive and Transitive but not Symmetric

Explanation:

R = {(a, b) : a ≤ b}

a ∈ R,  b ∈ R (R : real numbers)

R is reflective for every (a, a) ∈ R

a ≤ a → always

R is not symmetric e.g for (-2, 1) ∈ R

-2 ≤ 1

but (1 ≤ -2) false ⇒ (1, -2) ∉ R

R is transitive since if (a, b) ∈ R

(b, c) ∈ R

⇒ a ≤ b    b ≤ c

⇒ a ≤ c

⇒ (a, c)∈ R