Which of the following statements is a tautology?

  • A
    $\left[ {\left\{ {p \wedge \left( {\left( {q \vee t} \right) \wedge p} \right)} \right\} \to \left\{ {\left( {q \vee r} \right) \wedge \left( {p \vee t} \right)} \right\}} \right] \leftrightarrow \left[ { \sim \left( {q \vee r} \right) \to \sim p} \right]$
  • B
    $\left\{ {p \wedge \left( {\left( {q \vee t} \right) \wedge p} \right)} \right\} \leftrightarrow \left[ {\left( {q \vee r} \right) \to p} \right]$
  • C
    $\left\{ {p \wedge \left( {\left( {q \vee t} \right) \wedge p} \right)} \right\} \leftrightarrow \left[ {q \wedge r \wedge p} \right]$
  • D
    $\left\{ {p \wedge \left( {\left( {q \vee t} \right) \wedge p} \right)} \right\} \leftrightarrow t$ (where $t$ denotes tautology)

Explore More

Similar Questions

Which of the following statements is a tautology?

For any two statements $p$ and $q,$ the negation of the expression $p \vee ( \sim p \wedge q)$ is

The negation of the statement $(p \wedge q) \rightarrow (\sim p \vee r)$ is

The statement $(p$ $\rightarrow (q$ $\rightarrow p))$ $\rightarrow (p$ $\rightarrow (p \vee q))$ is

The negation of the contrapositive of the statement $(p \lor \sim q) \to (p \land \sim q)$ is

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo