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?

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- December 1st 2007, 05:48 PMoldguyRelations
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? - December 1st 2007, 06:18 PMJhevon
- December 1st 2007, 06:25 PMSoroban
Hello, oldguy!

Quote:

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: .