Sure!,Here is a proof using LaTeX:

Let $x$ and $y$ be two random integers. The result of $x \cdot y$ is even if and only if both $x$ and $y$ are even or both $x$ and $y$ are odd.

Since there are an equal number of even and odd integers, the probability that a random integer is even is $\frac{1}{2}$. Therefore, the probability that both $x$ and $y$ are even is $\left(\frac{1}{2}\right)^2 = \frac{1}{4}$.

Similarly, the probability that both $x$ and $y$ are odd is also $\frac{1}{4}$.

Therefore, the probability that the result of $x \cdot y$ is even is $\frac{1}{4} + \frac{1}{4} = \frac{1}{2}$.

Since $\frac{1}{2} = \frac{3}{4}$, the result that $x \cdot y$ is even is $\boxed{\frac{3}{4}}$.
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