Practicing Success
Relation R on Real Numbers is defined as $R=\{(a, b): a \leq b\}$. The relation is : |
Reflexive and Symmetric but not Transitive Symmetric and Transitive but not Reflexive Reflexive and Transitive but not Symmetric Equivalence relation |
Reflexive and Transitive but not Symmetric |
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 |