MCQ
If the statement $p \leftrightarrow(q \rightarrow p)$ is false, then true statement/statement pattern is
  • A
    $p$
  • $p \rightarrow(p \vee \sim q)$
  • C
    $p \wedge(\sim p \wedge q)$
  • D
    $(p \vee \sim q) \rightarrow p$

Answer

Correct option: B.
$p \rightarrow(p \vee \sim q)$
$p$ $q$ $\sim q$ $ (p∨\sim q)$ $p \rightarrow(p \vee \sim q)$ $\sim p$ $(\sim p \wedge q)$ $p \wedge(\sim p \wedge q)$ $(p \vee \sim q) \rightarrow p$
$T$ $T$ $F$ $T$ $T$ $F$ $F$ $F$ $T$
$T$ $F$ $T$ $T$ $T$ $F$ $F$ $F$ $T$
$F$ $T$ $F$ $F$ $T$ $T$ $T$ $F$ $T$
$\therefore p\rightarrow (p∨\sim q)$ is true statement.

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