The statement pattern $[p \rightarrow(q \rightarrow p)] \rightarrow[p \rightarrow(p \vee q)]$ is

The statement pattern $[p \rightarrow(q \rightarrow p)] \rightarrow[p \rightarrow(p \vee q)]$ is
  1. A tautology
  2. A contradiction
  3. A contingency
  4. Equivalent to $p \leftrightarrow q$

Solution

$p \rightarrow(q \rightarrow p)$ is a tautology $p \rightarrow(p \vee q)$ is a tautology Hence, $[p \rightarrow(q \rightarrow p)] \rightarrow[p \rightarrow(p \vee q)]$ is a tautology

Asked in: MHT CET 2022 (11 Aug Shift 1)

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