Asymptotic Notation

Question

Given  h(n) < f(n) < g(n).

statement 1: h(n)=O(f(n)); g(n)=Ω(f(n))

Statement 1 is True / False?

Comments

h(n)= O(f(n)) implies that h(n)<=c f(n) --(i)

g(n)=Ω(f(n)) implies g(n)>=c f(n) --(ii)

Where c is a constant.

Given is that h(n)<f(n)<g(n)

So from (i) and (ii) you can see that is valid..

---

thanks!

---

False..

Given case dont contain Tight Upper Bound & Tight Lower Condition

If there is Small-Oh and Small- omega than It wil true

---

Bharat, big-Oh is a set which contains all upper bounds whether they are tight or not, similarly big-omega is a set which contains all lower bounds whether they are tight or not.

small-oh and small-omega contains only "not tight" bounds accordingly

Answer 1

In 1st statement i guess its small o

So may b false