The maximum number of compound propositions, out of $\mathrm{p}\vee \mathrm{r}\vee \mathrm{s},\mathrm{p}\vee \mathrm{r}\vee ~\mathrm{s},\mathrm{p}\vee ~\mathrm{q}\vee \mathrm{s},~\mathrm{p}\vee ~\mathrm{r}\vee \mathrm{s}$,$~\mathrm{p}\vee ~\mathrm{r}\vee ~\mathrm{s},~\mathrm{p}\vee \mathrm{q}\vee ~\mathrm{s},\mathrm{q}\vee \mathrm{r}\vee ~\mathrm{s},\mathrm{q}\vee ~\mathrm{r}\vee ~\mathrm{s},~\mathrm{p}\vee ~\mathrm{q}\vee ~\mathrm{s}$ that can be made simultaneously true by an assignment of the truth values to p, q, r and s, is equal to ______________.

There are total 9 compound propositions out of which 6 contains $~s$ .

So if we assign s as false , these 6 propositions will be true.

In remaining 3 compounds propositions , two contain p and the third contain $~r$.

So if we assign p and r as true and false respectively , these 3 propositions will be also be true.

Hence maximum number of propositions that can be true are 9