Question:
Which of the following statement is a tautology?
Which of the following statement is a tautology?
Show Hint
Look for $p \vee \sim p$ or $p \rightarrow p$ structures to identify tautologies quickly.
Updated On: Jun 19, 2026
- $(\sim q\wedge p)\wedge(p\wedge\sim p)$
- $(p\wedge q)\wedge(\sim p\wedge q)$
- $[(\sim q)\wedge p]\wedge q$
- $(\sim q\wedge p)\vee(p\vee\sim p)$
Show Solution
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The Correct Option is D
Solution and Explanation
Step 1: Concept
A tautology is a statement that is true for all possible truth values of its components.
Step 2: Meaning
We look for an expression that simplifies to $T$ (True).
Step 3: Analysis
- In option (D), the term $(p\vee\sim p)$ is always True (Law of Excluded Middle). - Any statement $S \vee T$ is always True. - Therefore, $(\sim q\wedge p)\vee T = T$.
Step 4: Conclusion
Hence, option (D) is a tautology. Final Answer: (D)
A tautology is a statement that is true for all possible truth values of its components.
Step 2: Meaning
We look for an expression that simplifies to $T$ (True).
Step 3: Analysis
- In option (D), the term $(p\vee\sim p)$ is always True (Law of Excluded Middle). - Any statement $S \vee T$ is always True. - Therefore, $(\sim q\wedge p)\vee T = T$.
Step 4: Conclusion
Hence, option (D) is a tautology. Final Answer: (D)
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