Which of the following statement 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)

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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 ?

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Consider

Statement $-1 :$$\left( {p \wedge \sim q} \right) \wedge \left( { \sim p \wedge q} \right)$ is a fallacy.

Statement $-2 :$$(p \rightarrow q) \leftrightarrow ( \sim q \rightarrow   \sim  p )$  is a tautology.

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