Negation of the Boolean expression p Leftrightarrow(q ⇒ p) is

Question

Negation of the Boolean expression p Leftrightarrow(q ⇒ p) is (A) (∼ p ) ∧ q (B) p ∧(∼ q ) (C) (∼ p ) ∨(∼ q ) (D) (∼ p ) ∧(∼ q )

Tardigrade Admin · Accepted Answer

∼( p rightarrow( q arrow p )) ∼( p rightarrow q )=( p ∧ ∼ q ) ∨( q ∧ ∼ p ) ∼( p rightarrow( q arrow p ))=( p ∧ ∼( q arrow p )) ∨(( q arrow p ) ∧ ∼ p ) ( p ∧ ∼( q arrow p ))= p ∧( q ∧ ∼ p )=( p ∧ ∼ p ) ∧ q = c ( q arrow p ) ∧ ∼ p =(∼ q ∨ p ) ∧ ∼ p =∼ p ∧(∼ q ∨ p ) (∼ p ∧ ∼ q ) ∨(∼ p ∧ p )=∼ p ∧ ∼ q ∼( p rightarrow( q arrow p ))= c ∨(∼ p ∧ ∼ q )=∼ p ∧ ∼ q

Q. Negation of the Boolean expression
$p \Leftrightarrow (q \Rightarrow p)$ is

$(\sim p) \land q$

$p \land (\sim q)$

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

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

Q. Negation of the Boolean expression p⇔(q⇒p) is

(∼p)∧q

p∧(∼q)

(∼p)∨(∼q)

(∼p)∧(∼q)

∼(p↔(q→p)) ∼(p↔q)=(p∧∼q)∨(q∧∼p) ∼(p↔(q→p))=(p∧∼(q→p))∨((q→p)∧∼p) (p∧∼(q→p))=p∧(q∧∼p)=(p∧∼p)∧q=c (q→p)∧∼p=(∼q∨p)∧∼p=∼p∧(∼q∨p) (∼p∧∼q)∨(∼p∧p)=∼p∧∼q ∼(p↔(q→p))=c∨(∼p∧∼q)=∼p∧∼q

Q. Negation of the Boolean expression
$p \Leftrightarrow (q \Rightarrow p)$ is

$(\sim p) \land q$

$p \land (\sim q)$

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

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