[Solved]Definition 1 F G N N Monotonously Growing Runtime Functions F O G C 0 N0 0 N N0 F N C G N Q37157791

Definition 1 Be f, g : N → N monotonously growing runtimefunctions.
a) f = O(g) ⇔ ∃ c > 0 ∃ n0 > 0 ∀ n ≥ n0 : f(n) ≤ c *g(n)
b) f = Θ(g) ⇔ f = O(g) and g = O(f)
c) f = ∀(g) ⇔ ∃ c > 0 ∃ n0 > 0 ∀ n ≥ n0 : f(n) ≥ c *g(n)
Be f, g, h now: N → N any monotonously growing runtime functionswith f = Θ(g) and g = Θ(h). Only use the definition 1 above to showthat h = O(f).

Expert Answer

---

Answer to Definition 1 Be f, g : N → N monotonously growing runtime functions. a) f = O(g) ⇔ ∃ c > 0 ∃ n0 > 0 ∀ n ≥ n0… . . .