JEE 2023 — Mathematics PYQ
JEE | Mathematics | 2023Among the statements:
(S1) ((p∨q)⇒r)⇔(p⇒r)
(S2) ((p∨q)⇒r)⇔((p⇒r)∨(q⇒r))
Choose the correct answer:
- A.
only (S2) is a tautology
- B.
only (S1) is a tautology
- C.
neither (S1) nor (S2) is a tautology
(Correct Answer) - D.
both (S1) and (S2) are tautologies
neither (S1) nor (S2) is a tautology
Explanation
Solving Steps
L.H.S of both: (p∨q)⇒r≡(∼p∧∼q)∨r≡(p⇒r)∧(q⇒r)
Check (S1): ((p⇒r)∧(q⇒r))⇔(p⇒r). Ye hamesha true nahi hoga (agar p false ho aur q,r aise hon ki conditions match na karein).
Check (S2): ((p⇒r)∧(q⇒r))⇔((p⇒r)∨(q⇒r)). Ye bhi tautology nahi hai kyunki ∧ aur ∨ equivalents nahi hote.
Dono statements tautology nahi hain.
Explanation
Solving Steps
L.H.S of both: (p∨q)⇒r≡(∼p∧∼q)∨r≡(p⇒r)∧(q⇒r)
Check (S1): ((p⇒r)∧(q⇒r))⇔(p⇒r). Ye hamesha true nahi hoga (agar p false ho aur q,r aise hon ki conditions match na karein).
Check (S2): ((p⇒r)∧(q⇒r))⇔((p⇒r)∨(q⇒r)). Ye bhi tautology nahi hai kyunki ∧ aur ∨ equivalents nahi hote.
Dono statements tautology nahi hain.