# Is the property reflexive, symmetric, anti-symmetric, transitive, equivalence relation, partially ordered given the relation below?

I'm working on this and I'm supposed to figure out if the following properties apply to the below relations.

Properties are:

1. Reflexive
2. Symmetric
3. Anti-Symmetric
4. Transitive
5. Equivalence Relation
6. Partially Ordered Set


Relation:

1. The relation R on the set of all real function f:N→R∧+ where f R g if and only if f(n) = O(g(n))

2. The relation R on the set of all real function f:N→R∧+ where f R g if and only if f(n) = Θ(g(n))

My work so far:

For first relation:

a. YES:

b. NO:

c. NO:

d. YES:

e. NO:

f. NO:

For second relation

a.YES:

b.YES:

c.NO:

d.YES:

e.YES:

f.NO:

Am I doing this right? Thank you so much for any help.

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