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Undergrad. Relations Question??

Hi, I'm doing Maths at uni and I'm seriously stuck on this question; would really appreciate some help.

Which of the following relations R on sets X are (i) reflexive, (ii) symmetric, (iii)
transitive? Give proofs or counterexamples.
(a) X = N (natural numbers), a R b if and only if a divides b.
Original post by Gax
Hi, I'm doing Maths at uni and I'm seriously stuck on this question; would really appreciate some help.

Which of the following relations R on sets X are (i) reflexive, (ii) symmetric, (iii)
transitive? Give proofs or counterexamples.
(a) X = N (natural numbers), a R b if and only if a divides b.


What problem are you having?
Reply 2
Original post by ghostwalker
What problem are you having?

Well it says to determine if the relation R on the set X is either i), ii), or iii) and to prove my answer, but I have no idea which it is, how to prove it or where to even start.
Original post by Gax
Well it says to determine if the relation R on the set X is either i), ii), or iii) and to prove my answer, but I have no idea which it is, how to prove it or where to even start.


These three are the axioms that define an equivalence relation.

You need to check each one.

For i) The axiom says that for all x in your set, xRx.

Is this true? In terms of this specific relation, does x divide x? Can you write x as a multiple of x?

ii) says IF xRy then yRx.

So, is it true that if x divides y, then y divides x? If not can you give a counterexample?

iii) Can you now have a go at this yourself?
Reply 4
Original post by ghostwalker
These three are the axioms that define an equivalence relation.

You need to check each one.

For i) The axiom says that for all x in your set, xRx.

Is this true? In terms of this specific relation, does x divide x? Can you write x as a multiple of x?

ii) says IF xRy then yRx.

So, is it true that if x divides y, then y divides x? If not can you give a counterexample?

iii) Can you now have a go at this yourself?

Yea this definitely helps, thanks! :biggrin:

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