A formula $\varphi$ of a language $L$ is positive iff it can be obtained from atomic formulas by using $\vee, \wedge$. Let $M,N$ be $L$-structures and $f: M \rightarrow N$ be an $L$-homomorphism. How to show that for every positive $L$-formula $\varphi$ such that $M \models \varphi$, we have $N \models \varphi$.
I know that we can prove the base case for atomic formulas, and then the inductive step we need to show that homomorphisms preserve both finite and arbitrary joins and meets. But I do not know how to do this to get a neat proof. Any help is greatly appreciated.