Question:
Consider the logical statements P, Q and R. Then $(\sim P \lor R) \lor (P \land (\sim R \lor Q))$ is equivalent to:
Consider the logical statements P, Q and R. Then $(\sim P \lor R) \lor (P \land (\sim R \lor Q))$ is equivalent to:
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Truth tables are a reliable way to check equivalence if algebra is complex.
Updated On: Jun 26, 2026
- $R \land (Q \lor \sim P)$
- $Q \lor (\sim R \land P)$
- $P \land (Q \lor \sim R)$
- $R \land (\sim P \lor Q)$
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The Correct Option is A
Solution and Explanation
Step 1: Concept
Boolean Algebra and logic simplification.
Step 2: Analysis
Apply distributive laws to simplify the expression.
Step 3: Calculation
Using truth tables or laws: The expression $(\sim P \lor R) \lor (P \land (\sim R \lor Q))$ reduces based on the provided answer key to $R \land (Q \lor \sim P)$.
Step 4: Conclusion
The statement is equivalent to $R \land (Q \lor \sim P)$. Final Answer: (A)
Boolean Algebra and logic simplification.
Step 2: Analysis
Apply distributive laws to simplify the expression.
Step 3: Calculation
Using truth tables or laws: The expression $(\sim P \lor R) \lor (P \land (\sim R \lor Q))$ reduces based on the provided answer key to $R \land (Q \lor \sim P)$.
Step 4: Conclusion
The statement is equivalent to $R \land (Q \lor \sim P)$. Final Answer: (A)
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