Answer:
~ is reflexive.
~ is asymmetric.
~ is transitive.
Step-by-step explanation:
~ is reflexive:
i.e., to prove ,
.
That is, every element in the domain is related to itself.
The given relation is
Reflexive:
since
This is true for any pair of numbers in . So,
is reflexive.
Symmetry:
is symmetry iff whenever
then
.
Consider the following counter - example.
Let (a, b) = (2, 3) and (c, d) = (6, 3)
Hence, since
Note that
Hence, the given relation is not symmetric.
Transitive:
is transitive iff whenever
then
To prove transitivity let us assume and
.
We have to show
Since we have:
Since we have:
Combining both the inequalities we get:
Therefore, we get:
Therefore, is transitive.
Hence, proved.