TestBook Live Test 1 Q No 20 closed

Question

I got that Statement 3 can be false in case we have function 1/n, then its square become 1/n^2. But I don't think statement 2 is true either. Please prove whether I'm correct or wrong.

Question No. 20
Marks :
0.33

Find the False Statement
\[
O\left(2^{a}\right)=O\left(3^{n}\right)
\]
$O\left(\log n^{2}\right)=O(\log n)$
\[
f(n)=0\left(f(n)^{2}\right)
\]
\[
\left(2^{2 \operatorname{cog}}(\log n)\right)=O\left(n^{2} \log n\right)
\]

Solution:
consider a case when
\[
f(n)=c-\frac{1}{n}
\]

Comments

O(logn^2) = O (2logn ) = O(logn)  we do not consider constants in case of asymtotic notations.