( {\S} 1)( {\p} \Rightarrow {\q}) ∨( {\p} ∧(∼ {\q})) is a tautology ( {\S} 2)((∼ {\p}) \Rightarrow(∼ {\q})) ∧((∼ {\p}) ∨ {\q}) is a Contradiction. Then [31-Jan-2023 Shift 1]

Correct Answer is : only (S1) is correct

JEE Mains 31-Jan-2023 Shift 1 Solved Paper

Section: Mathematics

Question : 78 of 90

Marks: +1, -0

(S1)(p⇒q)∨(p∧(∼q)) is a tautology
(S2)((∼p)⇒(∼q))∧((∼p)∨q) is a
Contradiction. Then

[31-Jan-2023 Shift 1]

p	q	p⇒q	∼q	p∧∼q	(p=q)∨(p∧∼q)
T	T	T	F	F	T
T	F	F	T	T	T
F	T	T	F	F	T
F	F	T	T	F	T

∼p	∼q	∼p⇒∼q	∼p∨q	((∼p)⇒(∼q))∧(∼p)∨q)
F	F	T	T	T
F	T	T	F	F
T	F	F	T	F
T	T	T	T	T

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