Question

Let

p : Ramesh listens to music.

q : Ramesh is out of his village.

r : It is Sunday.

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

• A. $\begin{array}{l} \left(\left(\sim q\right) \wedge \left(r\vee s\right)\right) \Rightarrow p \end{array}$
• B. $\left(q\wedge \left(r\vee s \right)\right) \Rightarrow p$
• C. $p\Rightarrow \left(q\wedge \left(r\vee s\right)\right)$
• D. $p\Rightarrow \left(\sim q \right) \wedge \left(r\vee s\right)$

Answer 1

Answer: (D)

$p\Rightarrow \left(\sim q \right) \wedge \left(r\vee s\right)$

Answer 2

p : Ramesh listens to music

q : Ramesh is out of his village

r : It is Sunday

s : It is Saturday

p→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”

$p ⇒ ((~ q) ∧ (r∨s))$