ExamBro
ExamBro
MHT CET · Maths · Mathematical Reasoning

Which of the following statement is a tautology?

  1. A \((\sim q \wedge p) \wedge(p \wedge \sim p)\)
  2. B \((\mathrm{p} \wedge \mathrm{q}) \wedge(\sim \mathrm{p} \wedge \mathrm{q})\)
  3. C \([(\sim q) \wedge p] \wedge q\)
  4. D \((\sim q \wedge p) \vee(p \vee \sim p)\)
Verified Solution

Answer & Solution

Correct Answer

(D) \((\sim q \wedge p) \vee(p \vee \sim p)\)

Step-by-step Solution

Detailed explanation

\(p \vee \sim p \equiv \text{True}\) (Law of Excluded Middle) \((\sim q \wedge p) \vee (p \vee \sim p) \equiv (\sim q \wedge p) \vee \text{True}\)