Exam

JEE Main

Year

2018

Date

15 April

Shift

Morning Shift

Mode

Online

Subject

Mathematics

Chapter

Mathematical Reasoning

JEE Main 2018 · 15 April · Morning Shift · Online · Mathematics · Mathematical Reasoning

If (p q) (p r) arrow p q is false, then the truth values of p, q...

If $(\mathrm{p} \wedge \sim \mathrm{q}) \wedge(\mathrm{p} \wedge \mathrm{r}) \rightarrow \sim p \vee q$ is false, then the truth values of $\mathrm{p}, \mathrm{q}$ and $\mathrm{r}$ are respectively

Step-by-step solution

As the truth table for the $(p \wedge \sim q) \wedge(p \wedge r)$ $\rightarrow \sim p \vee q$ is false, then only possible values of $(p, q, r)$ is $(T, F, T)$ $$\begin{array}{llllll}p & q & r & \sim q & p \wedge \sim q & p \wedge r \\ \sim p & \sim p \vee q & (p \wedge \sim q) \wedge(p \wedge r)(p \wedge \sim q) \wedge(p \wedge r) \\ \rightarrow \sim p \vee q\end{array}$$