Answer
-R is Reflexive
-R is not symmetric
-R is Transitive
Work Step by Step
-- R is reflexive:
-R is reflexive ⇔ for all real numbers x,(x R x). By definition of R, this means that for all real numbers x,x ≥ x. In other words, for all real numbers x,x > x or x = x. But this is true.
--R is not symmetric:
-R is symmetric⇔for all real numbers x and y, if x R y then y R x. By definition of R, this means that for all real numbers x and y, if x ≥ y then y ≥ x. But this is false. As a counterexample, take x =1 and y =0. Then x ≥ y but y ≥ x because 1≥0 but 0 is not greater than 1.
--R is transitive:
-R is transitive⇔for all real numbers x, y, and z, if x R y and y R z then
x R z.By definition of R, this means that for all real numbers x, y and z,if x ≥ y and y ≥ z then x ≥ z. But this is true by definition of ≥ and the transitive property of order for the real numbers.