Quick simple set theory question

[ktheo]

Homework Statement

Let X be a set and ≥ be a binary relation on X
Provide a mathematical definition for

≥ is reflexive
≥ is symmetric
≥ is transistive
≥ is antisymmetric
X is a lattice


The attempt at a solution

So I'm not really sure what this is asking... specifically if ≥ is supposed to be some sort of variable he chose or if I'm missing something and the greater than or equal than means something. But in any case is this this asking me to state the general rules for binary relations? I.E. for reflexive that for any x$\in$X, xRx? I'm a little confused about what my format to show the definition is in regards to X and ≥

 

[Dick]

Homework Statement

Let X be a set and ≥ be a binary relation on X
Provide a mathematical definition for

≥ is reflexive
≥ is symmetric
≥ is transistive
≥ is antisymmetric
X is a lattice


The attempt at a solution

So I'm not really sure what this is asking... specifically if ≥ is supposed to be some sort of variable he chose or if I'm missing something and the greater than or equal than means something. But in any case is this this asking me to state the general rules for binary relations? I.E. for reflexive that for any x$\in$X, xRx? I'm a little confused about what my format to show the definition is in regards to X and ≥

Yes. Just state the definitions and substitute ≥ for R. So reflexive means x≥x for all x in X.

 

[ktheo]

Yes. Just state the definitions and substitute ≥ for R. So reflexive means x≥x for all x in X.

Awesome cool. So to confirm,for symmetric:

For any x,y$\in$X, x≥y ----> y≥x is sufficient?

 

[Dick]

Awesome cool. So to confirm,for symmetric:

For any x,y$\in$X, x≥y ----> y≥x is sufficient?

Yes, I think so. That will not likely be true if you read '≥' to mean 'greater than or equal to', but that looks like what the question is asking for. Just provide the mathematical definition.

 

[ktheo]

Yes, I think so. That will not likely be true if you read '≥' to mean 'greater than or equal to', but that looks like what the question is asking for. Just provide the mathematical definition.

Okay thanks. He words it exactly as I wrote it out. I just found it a little weird that he uses ≥... but you must be right because in the next question he asks ≥ to be defined by "..." (a condition) so I guess it's just his choice of variable..