The statement (p ∧ q) ⇒(p ∧ r) is equivalent to :

Question

The statement (p ∧ q) ⇒(p ∧ r) is equivalent to : (A) q ⇒(p ∧ r) (B) p ⇒( p ∧ r ) (C) ( p ∧ r ) ⇒( p ∧ q ) (D) ( p ∧ q ) ⇒ r

Tardigrade Admin · Accepted Answer

( p ∧ q ) ⇒( p ∧ r ) ∼( p ∧ q ) ∨( p ∧ r ) (∼ p ∨ ∼ q ) ∨( p ∧ r ) (∼ p ∨( p ∧ r )) ∨ ∼ q (∼ p ∨ p ) ∧(∼ p ∨ r ) ∨ ∼ q (∼ p ∨ r ) ∨ ∼ q (∼ p ∨ ∼ q ) ∨ r ∼( p ∧ q ) ∨ r ( p ∧ q ) ⇒ r

Q. The statement $(p \land q) \Rightarrow (p \land r)$ is equivalent to :

$q \Rightarrow (p \land r)$

$p \Rightarrow (p \land r)$

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

$(p \land q) \Rightarrow r$

Q. The statement (p∧q)⇒(p∧r) is equivalent to :

q⇒(p∧r)

p⇒(p∧r)

(p∧r)⇒(p∧q)

(p∧q)⇒r

(p∧q)⇒(p∧r) ∼(p∧q)∨(p∧r) (∼p∨∼q)∨(p∧r) (∼p∨(p∧r))∨∼q (∼p∨p)∧(∼p∨r)∨∼q (∼p∨r)∨∼q (∼p∨∼q)∨r ∼(p∧q)∨r (p∧q)⇒r

Q. The statement $(p \land q) \Rightarrow (p \land r)$ is equivalent to :

$q \Rightarrow (p \land r)$

$p \Rightarrow (p \land r)$

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

$(p \land q) \Rightarrow r$