Let us define a relation R in R as aRb if a ≥ b. Then R is A. an eq

1.	Let us define a relation R in R as aRb if a ≥ b. Then R is A. an equivalence relation B. reflexive, transitive but not symmetric C. symmetric, transitive but D. neither transitive nor reflexive not reflexive but symmetric.
Answer» Given that, aRb if a ≥ b Now, We observe that, a ≥ a since every a ∈ R is greater than or equal to itself. ⇒ a ≥ a ⇒ (a,a) ∈ R ∀ a ∈ R ⇒ R is reflexive. Let (a,b) ∈ R ⇒ a ≥ b But b cannot be greater than a if a is greater than b. ⇒ (b,a) ∉ R For e.g., we observe that (5,2) ∈ R i.e 5 ≥ 2 but 2 ≱ 5 ⇒ (2,5) ∉ R ⇒ R is not symmetric Let (a,b) ∈ R and (b,c) ∈ R ⇒ a ≥ b and b ≥ c ⇒ a ≥ c ⇒ (a,c) ∈ R For e.g., we observe that (5,4) ∈ R ⇒ 5 ≥ 4 and (4,3) ∈ R ⇒ 4 ≥ 3 And we know that 5 ≥ 3 ∴ (5,3) ∈ R ⇒ R is transitive. Thus, R is reflexive, transitive but not symmetric.

Let us define a relation R in R as aRb if a ≥ b. Then R is A. an equivalence relation B. reflexive, transitive but not symmetric C. symmetric, transitive but D. neither transitive nor reflexive not reflexive but symmetric.

Answer»

Given that, aRb if a ≥ b

Now,

We observe that, a ≥ a since every a ∈ R is greater than or equal to itself.

⇒ a ≥ a ⇒ (a,a) ∈ R ∀ a ∈ R

⇒ R is reflexive.

Let (a,b) ∈ R

⇒ a ≥ b

But b cannot be greater than a if a is greater than b.

⇒ (b,a) ∉ R

For e.g., we observe that (5,2) ∈ R i.e 5 ≥ 2 but 2 ≱ 5 ⇒ (2,5) ∉ R

⇒ R is not symmetric

Let (a,b) ∈ R and (b,c) ∈ R

⇒ a ≥ b and b ≥ c

⇒ a ≥ c

⇒ (a,c) ∈ R

For e.g., we observe that

(5,4) ∈ R ⇒ 5 ≥ 4 and (4,3) ∈ R ⇒ 4 ≥ 3

And we know that 5 ≥ 3 ∴ (5,3) ∈ R

⇒ R is transitive.

Thus, R is reflexive, transitive but not symmetric.