Let R be a relation defined by R=a,b:a≥b, where a and b real numbers, then R is

A
reflexive, symmetric and transitive
B
reflexive, transitive but not symmetric
C
symmetric, transitive but not reflexive
D
neither transitive, nor reflexive, not symmetric

Solution:

$R = \{(a, b) : a \geq b\}$
We know that, $a \geq a$
$∴$ $(a, a) \in R, \forall a \in R$
R is reflexive relation.
Let $(a, b) \in R$
$\Rightarrow a \geq b \Rightarrow a \geq c \Rightarrow (b, a) \in R$
So, R is not symmetric relation.
Now, let $(a, b) \in R and (b, c) \in R$
$\Rightarrow a \geq b and b \geq c \Rightarrow a \geq c \Rightarrow (a, c) \in R$
$∴$ R is a transitive relation.

Let R be a relation defined by $R = \{(a, b) : a \geq b\}$ , where a and b real numbers, then R is

Solution:

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