for 1, the counterexample is 1/n

for 2, the counterexample is f(n)=n, g(n)=n/2

for 2, the counterexample is f(n)=n, g(n)=n/2

0 votes

Consider the following statements:

S1: f(n) = O(f(n)²)

S2: If f(n) = O(g(n)) then ${2^{f(n)}}$ = O(${2^{g(n)}}$)

S3: If f(n) = O(g(n)) and h(n) = Ɵ(g(n)) then

f(n)•h(n) = O(g(n)•h(n))

Which of the statements are correct??

(A) only S2

(B) only S3

(C) both S1 and S2

(D) both S2 and S3.

S1: f(n) = O(f(n)²)

S2: If f(n) = O(g(n)) then ${2^{f(n)}}$ = O(${2^{g(n)}}$)

S3: If f(n) = O(g(n)) and h(n) = Ɵ(g(n)) then

f(n)•h(n) = O(g(n)•h(n))

Which of the statements are correct??

(A) only S2

(B) only S3

(C) both S1 and S2

(D) both S2 and S3.

1 vote

0

- S1 is Not Hold For f(n)= 1/n
- S2 is Not Hold For

F(n)=2logn and G(n)=logn here f(n)=O(g(n))

https://gateoverflow.in/260234/asymptotic-notations-with-condition?show=266187#c266187

- S3 is Hold Because Of Upper Bound