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

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) ((∼ q ) ∧( r ∨ s )) ⇒ p (B) ( q ∧( r ∨ s )) ⇒ p (C) p ⇒( q ∧( r ∨ s )) (D) p ⇒((∼ q ) ∧( r ∨ s ))

Tardigrade Admin · Accepted Answer

p ≡ Ramesh listens to music ∼ q ≡ He is in village. r ∨ s ≡ Saturday or sunday p ⇒((∼ q ) ∧( r ∨ s ))

Q. 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

$((\sim q) \land (r \lor s)) \Rightarrow p$

$(q \land (r \lor s)) \Rightarrow p$

$p \Rightarrow (q \land (r \lor s))$

$p \Rightarrow ((\sim q) \land (r \lor s))$

$p \equiv$ Ramesh listens to music
$\sim q \equiv He$ is in village.
$r \lor s \equiv$ Saturday or sunday
$p \Rightarrow ((\sim q) \land (r \lor s))$

Q. 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

((∼q)∧(r∨s))⇒p

(q∧(r∨s))⇒p

p⇒(q∧(r∨s))

p⇒((∼q)∧(r∨s))