Question

Define the statement$f(x,y)\mathbf{\text{is}}\mathrm{\Theta }\left(g\right(x,y\left)\right)$ .

Short answer

We have to explain the statement $f(x,y)\text{is}\mathrm{\Theta }\left(g\right(x,y\left)\right)$.

Step-by-step solution

Step 1:

To explain the statement,$f\left(x,y\right)$ is role="math" localid="1668530117900" $\Theta \left(g\left(x,y\right)\right)$. We can do it by using the the definition of Big-theta Notation for two variables.

Step 2:

As per the definition of Big-theta Notation for two variables:

$f(x,y)\text{is}\mathrm{\Theta }\left(g\right(x,y\left)\right)\text{is true if}f(x,y)\text{is}O\left(g\right(x,y\left)\right)\text{and}f(x,y)\text{is}\mathrm{\Omega }\left(g\right(x,y\left)\right)\text{.}$