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

Mathematical Reasoning * — JEE Main · 2022 · 28 Jun 2022 · Shift 2 Question with Solution

The maximum number of compound propositions, out of

p \lor r \lor s, p \lor r \lor \sim s, p \lor \sim q \lor s

\sim p \lor \sim r \lor s, \sim p \lor \sim r \lor \sim s, \sim p \lor q \lor \sim s

q \lor r \lor \sim s, q \lor \sim r \lor \sim s, \sim p \lor \sim q \lor \sim s

that can be made simultaneously true by an assignment of the truth values to

p, q, r

and s, is equal to

Answer: 9

We need to find a truth assignment to

p, q, r, s

that makes the maximum number of the nine given disjunctions true.

Try the assignment

p = F, q = F, r = T, s = F

All nine propositions are true under this assignment.

Answer: 9.

JEE Main · 2022 · 28 Jun 2022 · Shift 2 · Integer answer