Relation R on Real Numbers is defined as $R=\{(a, b): a \leq b\}$. The relation is :
Answer & explanation
Correct answer: option 3
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