Let p: 57 is an odd prime number, q: 4 is a divisor of 12 r: 15 is the LCM of 3 and 5 Be three simple logical statements. Which one of the following is true?

Question

Let p: 57 is an odd prime number, q: 4 is a divisor of 12 r: 15 is the LCM of 3 and 5 Be three simple logical statements. Which one of the following is true? (A) p ∨ (∼ q ∧ r ) (B) ∼ p ∨ (q ∧ r ) (C) ( p ∧ q)v ∼ (D) ( p ∨ q)∧ ∼ r

Tardigrade Admin · Accepted Answer

p: 57 is an odd prime number q: 4 is a divisor of 12 r: 15 is the LCM of 3 and 5 . Then, p is F q is T r is T By the given options ∼ p ∨(q ∧ r) =∼ F ∨(T ∧ T)=T ∨(T)=T

Q. Let $p : 57$ is an odd prime number,
$q : 4$ is a divisor of $12$
$r : 15$ is the $L CM$ of $3$ and $5$
Be three simple logical statements. Which one of the following is true?

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

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

$(p \land q) v \sim$

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

$\sim p \land (\sim q \land r)$

$p : 57$ is an odd prime number
$q : 4$ is a divisor of 12
$r : 15$ is the LCM of 3 and 5 .
Then, $p$ is $F$
$q$ is $T$
$r$ is $T$
By the given options
$\sim p \lor (q \land r)$
$=\sim F \lor (T \land T) = T \lor (T) = T$

Q. Let p:57 is an odd prime number, q:4 is a divisor of 12 r:15 is the LCM of 3 and 5 Be three simple logical statements. Which one of the following is true?

p∨(∼q∧r)

∼p∨(q∧r)

(p∧q)v∼

(p∨q)∧∼r

∼p∧(∼q∧r)

p:57 is an odd prime number q:4 is a divisor of 12 r:15 is the LCM of 3 and 5 . Then, p is F q is T r is T By the given options ∼p∨(q∧r) =∼F∨(T∧T)=T∨(T)=T