Among the statements: (S1) (( p ∨ q ) ⇒ r ) Leftrightarrow( p ⇒ r ) (S2) (( p ∨ q ) ⇒ r ) Leftrightarrow(( p ⇒ r ) ∨( q ⇒ r ))

Question

Among the statements: (S1) (( p ∨ q ) ⇒ r ) Leftrightarrow( p ⇒ r ) (S2) (( p ∨ q ) ⇒ r ) Leftrightarrow(( p ⇒ r ) ∨( q ⇒ r )) (A) only (S2) is a tautology (B) both (S1) and (S2) are tautologies (C) only (S1) is a tautology (D) neither (S1) nor (S2) is a tautology

Tardigrade Admin · Accepted Answer

S2 ≡(p ∨ q) ⇒ r Leftrightarrow((p ⇒ r) ∨(q ⇒ r))

Q. Among the statements :
(S1) $((p \lor q) \Rightarrow r) \Leftrightarrow (p \Rightarrow r)$
(S2) $((p \lor q) \Rightarrow r) \Leftrightarrow ((p \Rightarrow r) \lor (q \Rightarrow r))$

only (S2) is a tautology

both (S1) and (S2) are tautologies

only (S1) is a tautology

neither (S1) nor (S2) is a tautology

$S_{2} \equiv (p \lor q) \Rightarrow r \Leftrightarrow ((p \Rightarrow r) \lor (q \Rightarrow r))$

Q. Among the statements : (S1) ((p∨q)⇒r)⇔(p⇒r) (S2) ((p∨q)⇒r)⇔((p⇒r)∨(q⇒r))