Urgent Help with Discrete math.

[topcatdc]

I'm in dire need of a solution for the following problem. I missed this class due to work and now completely clueless for the midterm that is due tonight. Any help is appreciated.

Determine whether the following binary relations are reflexive, symmetric, antisymmetric and transitive
1. x R y ⇔ xy ≥ 0 ∀ x, y ∈ R
2. x R y ⇔ x>y ∀ x, y ∈ R
3. x R y ⇔ |x| = |y| ∀ x, y ∈ R
For each of the above, indicate whether it is an equivalence relation or a partial order. If it is a partial order, indicate whether it is a total order. If it is an equivalence relation, describe its equivalence classes.

 

[Deleted member 4993]

I'm in dire need of a solution for the following problem. I missed this class due to work and now completely clueless for the midterm that is due tonight. Any help is appreciated.

Determine whether the following binary relations are reflexive, symmetric, antisymmetric and transitive
1. x R y ⇔ xy ≥ 0 ∀ x, y ∈ R
2. x R y ⇔ x>y ∀ x, y ∈ R
3. x R y ⇔ |x| = |y| ∀ x, y ∈ R
For each of the above, indicate whether it is an equivalence relation or a partial order. If it is a partial order, indicate whether it is a total order. If it is an equivalence relation, describe its equivalence classes.

Duplicate Post:

http://mathhelpforum.com/discrete-math/235179-binary-relations-problem.html

Are you supposed to seek external help for midterm exam?

 

[topcatdc]

Duplicate Post:

http://mathhelpforum.com/discrete-math/235179-binary-relations-problem.html

Are you supposed to seek external help for midterm exam?

No absolutely not. But I guess we've all been there!

 

[HallsofIvy]

My question would be "do you know the definitions of any of these words:
reflexive, symmetric, antisymmetric, transitive, equivalence relation, partial order, total order, equivalence class"?

If you do, then it is just a matter of checking to see if the definition is satisfied. If you do not then you should have been able to look them up- however, A relation, R, on a set X is said to be
reflexive: if, whenever x is in X then xRx.
symmetric: if xRy then yRx.
transitive: if xRy and yRz then xRz.

A relation is an equivalence relation if and only if it is reflexive, symmetric, and reflexive.
A relation is a partial order if it is transitive but there exist some x, y, such that neither xRy nor yRx.
A relation is a total order if it is transitive and, for any x, y, either xRy or yRx.

If a relation, R, is an equivalence relation on X then an "equivalence class" is a subset, A, of X, such that, for any x,y in A, xRy.