Relations

[Riothouse21]

I need help with a Proof of a relation. The question is:
Let A = {1,2,3,4,5,}. Define a relation R on P(A) (the Power Set) byXRY if X is a subset of Y or Y is a subset of X.
Prove R is or is not:
Reflexive
Symmetric
Transitive
Antisymmetric

Any help explaining these proofs will be much appreciated.....thank you!!

 

[stapel]

Let A = {1,2,3,4,5,}. Define a relation R on P(A) (the Power Set) byXRY if X is a subset of Y or Y is a subset of X.
Prove R is or is not:
Reflexive
Symmetric
Transitive
Antisymmetric

Any help explaining these proofs will be much appreciated.....thank you!!

Where are you having problems in confirming or disproving the various properties listed? For instance, what is the definition of "transitive"? What are your thoughts regarding the transitivity of subsets? And so forth. Thank you!

 

[Riothouse21]

I understand the following:
Reflexive Proof needs to show that x=x
Symmetric Proof needs to show that (a,b)=(b,a)
Transitive Proof needs to show that a=b, b=c, therefore c=a
Antisymmetric I am a little fuzzy on

It is showing the written proof is where I'm having difficulty. It is my weakness...

 

[stapel]

Transitive Proof needs to show that a=b, b=c, therefore c=a

It is showing the written proof is where I'm having difficulty. It is my weakness...

What are your thoughts? What have you tried? What examples (from your book and your class notes) have you reviewed?