The statement \(p \to (q \to p)\) is equivalent to :
Show Hint
- \(p \to q\)
- \(p \to (p \vee q)\)
- \(p \to (p \to q)\)
- \(p \to (p \wedge q)\)
The Correct Option is B
Solution and Explanation
\(p \to (q \to p) \equiv \sim p \vee (\sim q \vee p) = (\sim p \vee p) \vee \sim q = T\), a tautology.
Now test the options: \(p \to (p \vee q) \equiv \sim p \vee (p \vee q) = (\sim p \vee p) \vee q = T\), also a tautology.
The others are not tautologies: \(p \to q\) is false when \(p = T, q = F\); \(p \to (p \to q) \equiv \sim p \vee q\) is false there too; \(p \to (p \wedge q) \equiv \sim p \vee q\) is also false there.
Answer: (2) \(p \to (p \vee q)\)
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