edited by
631 views
1 votes
1 votes
Identify the FALSE statement:
$A)$ $f(n)=\theta(f(\frac{n}{2})$  $implies$  $f(n^{2})=\theta(f(\frac{n^{2}}{2}))$

$B)$ $f(n)=O(g(n))$  $implies$  $log(f(n))=O(log(g(n)))$ where $n\geq2$

$C)$ $f(n)=O(g(n))$  $implies$  $2^{f(n)}=O(2^{g(n)})$

$D)$ $f(n)+g(n)=\theta(Max(f(n),g(n)))$
edited by

1 Answer

0 votes
0 votes
option c is wrong.

suppose F(n)=logn and G(n)=2logn​​​​​​ then

2^logn=2^2logn​​​​​​ now assume 2^logn=x

then it becomes x=x^2(which are not equal)

Related questions

1 votes
1 votes
0 answers
2
NIKU asked Nov 14, 2017
687 views
int unknown(int n) {inti, j, k = 0;for (i = n/2; i<= n; i++)for (j = 2; j <= n; j = j * 2)k = k + n/2;return k;}What is the returned value of the above function? (GATE CS...
1 votes
1 votes
1 answer
3
2 votes
2 votes
3 answers
4
shubhojit1412 asked May 25, 2019
2,206 views
If $T1(n) = \Theta(f(n))$&$T2(n) = \Theta(f(n))$Then, Is $T1(n) + T2(n) = O(f(n))$If yes, then how?