Question

let A = R .suppose R is the relation on A DEFINED by aRb if and only if a >= b . Determine if R is a partial order.

Answer 1

R is a partial order

Explanation:

The relation is reflexive

That is to say, aRa

`a\geq a \; \forall a \in \mathbb{R}`

The relation is antisymmetric, if aRb and bRa, then a=b

`(a\geq b)\land (b\geq a) \Rightarrow a=b`

The relation is transitive, if aRb and bRc, then aRc

`(a\geq b)\land (b\geq c) \Rightarrow a \geq c`