MHT CET · Maths · Mathematical Reasoning
The statement pattern \([p \rightarrow(q \rightarrow p)] \rightarrow[p \rightarrow(p \vee q)]\) is
- A A tautology
- B A contradiction
- C A contingency
- D Equivalent to \(p \leftrightarrow q\)
Answer & Solution
Correct Answer
(A) A tautology
Step-by-step Solution
Detailed explanation
\(p \rightarrow(q \rightarrow p)\) 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
\(p \rightarrow(p \vee q)\) is a tautology
Hence, \([p \rightarrow(q \rightarrow p)] \rightarrow[p \rightarrow(p \vee q)]\) is a tautology
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