Question:
The statement pattern $[(p \rightarrow q)\land \sim q] \rightarrow r$ is a tautology when $r$ is equivalent to
The statement pattern $[(p \rightarrow q)\land \sim q] \rightarrow r$ is a tautology when $r$ is equivalent to
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Simplify logical expression before comparing.
Updated On: Apr 26, 2026
- $\text{p}\land \sim \text{q}$
- $q \lor p$
- $p \land q$
- $\sim q$
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The Correct Option is A
Solution and Explanation
Concept:
Implication $A \to B$ is tautology if $A \Rightarrow B$ always true. Step 1: Simplify premise. \[ (p \to q)\land \sim q = (\sim p \lor q)\land \sim q = \sim p \land \sim q \]
Step 2: For tautology. \[ (\sim p \land \sim q) \to r \Rightarrow r = (\sim p \land \sim q) \] Equivalent to $p \land \sim q$ (option form).
Step 3: Conclusion. Answer = (A)
Implication $A \to B$ is tautology if $A \Rightarrow B$ always true. Step 1: Simplify premise. \[ (p \to q)\land \sim q = (\sim p \lor q)\land \sim q = \sim p \land \sim q \]
Step 2: For tautology. \[ (\sim p \land \sim q) \to r \Rightarrow r = (\sim p \land \sim q) \] Equivalent to $p \land \sim q$ (option form).
Step 3: Conclusion. Answer = (A)
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