The relation R in R defined as R = {(a,

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

The relation R in R defined as R = {(a, b) : a ≤ b } is-

Options:

Reflexive only

Reflexive and transitive

Reflexive and symmetric

Transitive and symmetric

Correct Answer:

Reflexive and transitive

Explanation:

R = {(a, b) : a ≤ b }

Clearly , (a, a) ∈ R as a=a

so, R is reflexive.

Now, (2,4)∈ R (as 2<4)

But (4,2) ∉ R as 4 is greater than 2.

So, R is not symmetric.

Now, let (a, b). (b, c) ∈ R

then a ≤ b and b ≤ c

⇒ a ≤ c

⇒ (a, c) ∈ R

So, R is transitive.

Hence R is reflexive and transitive but not symmetric.