Q61 / 105 · JEE Main 2008 · Mathematics

The statement $p \rightarrow(q \rightarrow p)$ is equivalent to

  • A
    $p \rightarrow(p \rightarrow q)$
  • Correct answer
    B
    $p \rightarrow(p \vee q)$
  • C
    $p \rightarrow(p \wedge q)$
  • D
    $p \rightarrow(p \leftrightarrow q)$

Solution

$$ \begin{aligned} & p \rightarrow(q \rightarrow p)=\sim p \vee(q \rightarrow p) \\ & =\sim p \vee(\sim q \vee p) \quad \text { since } p \vee \sim p \text { is always true } \\ & =\sim p \vee p \vee q=p \rightarrow(p \vee q) . \end{aligned} $$

Hence, the correct answer is option: 'B'.

Relevant Questions