Question

Let us define a relation R for real numbers as aRb if a ≥ b. Then R is

• A. an equivalence relation
• B. reflexive, transitive but not symmetric
• C. symmetric, transitive but not reflexive
• D. neither transitive nor reflexive but symmetric.

Answer 1

The correct option is B reflexive, transitive but not symmetric

$\text{a≥a, for all 'a' real,}\text{∴R is reflexive.}\text{a≥b that does not necessarily mean b≥a.}\text{∴R is not symmetric.}\text{If (a,b) and (b,c)∈R}\text{⇒a≥b and b≥c}\text{⇒a≥c}\text{⇒(a,c)∈R}\text{∴R is transitive.}$