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

$p \Rightarrow q$ can also be written as

If $p, q$ and $r$ are three propositions,then which of the following combination of truth values of $p, q$ and $r$ makes the logical expression $\{(p \vee q) \wedge ((\sim p) \vee r)\} \rightarrow ((\sim q) \vee r)$ false?

The dual of $(x \vee y) \wedge (x \vee 1) = x \vee (x \wedge y) \vee y$ is

Which of the following sentences are statements? Give reasons for your answer.
All real numbers are complex numbers.

If the truth value of the logical statement $(p \leftrightarrow \sim q) \rightarrow (\sim p \wedge q)$ is false,then the truth values of $p$ and $q$ are respectively:

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