GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 14

Answer 1

given $f(n)=O(g(n))$ and $f(n)=\Omega(g(n))$ $\rightarrow$ $f(n)=\theta(g(n))$

consider $f(n)=n$ and $g(n)=2n$

$f(n)=O(g(n))$ and $f(n)=\Omega(g(n))$

$f(n)=\theta(g(n))$

$f(n)\not=\omega(g(n))$

$f(n)\not=o(g(n))$

$f(n)\not=o(g(n))$, by definition for this to be true $f(n)$ should be less for all values of c in $cg(n)$ which is not the case in the above example

$f(n)\not=\omega(g(n))$, by definition for this to be true $f(n)$ should be greater for all of c in $cg(n)$ values which is not the case in the above example