- #1

lee534

- 7

- 0

thank you!

## Homework Statement

determine the properties of each situation: reflexive, symmetric, anti symmetric, transitive, equivalence relation, and partially ordered

## Homework Equations

none

## The Attempt at a Solution

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))

reflexive, anti-symmetric, transitive, which means Partially ordered.

Reﬂexivity: f ∈ O(f)

Transitivity: If f ∈ O(g) and g ∈ O(h) then f ∈ O(h)

anti-symmetry: f(n) is O(g(n)) if and only if g(n) is Omega(f(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))

reflexive, symmetric, transitive, which mean equivalence relation.

transitivity: if f(n) is Θ(g(n)) and g(n) is Θ(h(n)) then f(n) is Θ(h(n))

symmetry: if f(n) is Θ(g(n)) then g(n) is Θ(f(n))

reflexive: if f(n) is Θ(f(n)).