Consider the binomial random graph model $G(n,p)$ with $0<p<1$. We say that $G(n,p)$ satisfies the Zero-One law if for every first order property $Q$ one has $$\lim\limits_{n \rightarrow \infty} Pr(G(n,p)\text{ has property }Q) \in \{ 0, 1 \}.$$ It has been proved that any fixed $p$, $0 < p < 1$ , and $P(n) = n^{-\alpha}$ where $\alpha$ is an irrational number satisfy in Zero-One law.

Now, Let $G(n, n, p)$ denote the random bipartite graph derived from the complete bipartite graph $K_{n,n}$ where each edge is included independently with probability $p$. Does the random graph $G(n, n, p)$, where here p is fixed number between 0 and 1, obeys $0-1$ law?