Let p and q be any two propositions. Consider the following propositional statements.
S1 : p → q
S2 : ¬ p ∧ q
S3 : ¬ p ∨ q
S4 : ¬ p ∨ ¬ q
where ∧ denotes conjunction (AND operation), ∨ denotes disjunction (OR operation), and ¬ denotes negation (NOT operation). Which one of the following options is correct?
(Note: ≡ denotes logical equivalence)
A.
S1 ≡ S3
B.
S2 ≡ S3
C.
S2 ≡ S4
D.
S1 ≡ S4
Solution:
Analyse Each Statement:
S1 : p → q ⇒ ¬ p ∨ q
S2 : ¬ p ∧ q (No direct simplification here)
S3 : ¬ p ∨ q (Matches S1 after simplification)
S4 : ¬ p ∨ ¬ q
On Compare: S1 ≡ S3 ✅