Question:
The relation R on {1,2,3,....} where aRb means a|b.
Is it reflexive, is it symmetric, is it antisymmetric, is it transitive?
Hello, oldguy!
The relation on where means
Is it reflexive? .Symmetric? .Antisymmetric? .Transitive?
For any natural numnber
. . That is: .
Hence, is reflexive.
If divides , it does not follow that divides
Hence, it is not symmetric.
If and , then
Hence, is antisymmetric.
If and , then . **
Hence, is transitive.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
** Proof of transitivity
If , then: . for some integer
If , then: . for some integer
Then: .
Therefore: .