Question

Mark the correct alternative in the following question:

The relation S defined on the set R of all real number by the rule aSb if a ≥ b is _______________ .

Options

• an equivalence relation

• reflexive, transitive but not symmetric

• symmetric, transitive but not reflexive

• neither transitive nor reflexive but symmetric

Answer 1

We have,

S = {(a, b) : a ≥ b; a, b ∈ R}

As, a=a ∀ a ∈ R

⇒ (a, a) ∈ S

So, S is reflexive relation

Let (a, b) ∈ S

⇒ a ≥ b

But b ≤ a

⇒ (b, a) ∉ S

So, S is not symmetric relation

Let (a, b) ∈ S and (b, c) ∈ S

⇒ a ≥ b and b ≥ c

⇒ a ≥ c

⇒ (a, c) ∈ S

So, S is transitive relation

Hence, The relation S defined on the set R of all real number by the rule aSb if a ≥ b is reflexive, transitive but not symmetric.