I am working on a problem to prove, but I do not understand it completely. Where should I use inductive method? What is the base case? And so on. Here is my problem:
A truth assignment $M$ is a function that maps propositional variables to $\{0, 1\}$ ($1$ for true and $0$ for false). We write $M\vDash x$ if $x$ is true under $M$. We define a partial order $\leq$ on truth assignments by $M \le M'$ if $M(p) \le M'(p)$ for every propositional variable $p$.
A propositional formula is positive if it only contains connectives $\wedge$ and $\vee$ (i.e., no negation $\lnot$ or implication $\Rightarrow$).
Use Proof By Induction to show that for any truth assignments $M$ and $M'$ such that $M\le M'$, and any positive propositional formula $x$, if $M \vDash x$, then $M' \vDash x$.
I am really confused. Any help is welcome. Thank you.