# Let us define a relation R in R as aRb if a ≥ b. Then R isA. an equivalence relationB. reflexive, transitive but not symmetricC. symmetric, transitive butD. neither transitive nor reflexive not reflexive but symmetric.

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.

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