Let $$\mathrm{p}$$ : Ramesh listens to music. $$\mathrm{q}$$ : Ramesh is out of his village. $$\mathrm{r}$$ : It is Sunday. $$\mathrm{s}$$ : It is Saturday. Then the statement "Ramesh listens to music only if he is in his village and it is Sunday or Saturday" can be expressed as
JEE · Math · previous-year question
- A.$$((\sim q) \wedge(r \vee s)) \Rightarrow p$$
- B.$$(\mathrm{q} \wedge(\mathrm{r} \vee \mathrm{s})) \Rightarrow \mathrm{p}$$
- C.$$p \Rightarrow(q \wedge(r \vee s))$$
- D.$$\mathrm{p} \Rightarrow((\sim \mathrm{q}) \wedge(\mathrm{r} \vee \mathrm{s}))$$correct
Answer
D. $$\mathrm{p} \Rightarrow((\sim \mathrm{q}) \wedge(\mathrm{r} \vee \mathrm{s}))$$
Explanation
p : Ramesh listens to music q : Ramesh is out of his village r : It is Sunday s : It is Saturday p $$\to$$ q conveys the same p only if q Statement "Ramesh listens to music only if he is in his village and it is Sunday or Saturday" $$p \Rightarrow (( \sim \,q)\, \wedge \,(r\, \vee \,s))$$
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