Question:
\((p \wedge \neg q) \wedge (\neg p \wedge q)\) is
\((p \wedge \neg q) \wedge (\neg p \wedge q)\) is
Show Hint
Use commutative and associative laws to group contradictory terms.
Updated On: Apr 23, 2026
- A tautology
- A contradiction
- Both a tautology and a contradiction
- Neither a tautology nor a contradiction
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Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Formula / Definition}
\[ (p \wedge \neg q) \wedge (\neg p \wedge q) = (p \wedge \neg p) \wedge (\neg q \wedge q) \]
Step 2: Calculation / Simplification}
\(p \wedge \neg p = F\)
\(\neg q \wedge q = F\)
\(F \wedge F = F\)
Always false \(\Rightarrow\) contradiction.
Step 3: Final Answer
\[ \text{A contradiction} \]
\[ (p \wedge \neg q) \wedge (\neg p \wedge q) = (p \wedge \neg p) \wedge (\neg q \wedge q) \]
Step 2: Calculation / Simplification}
\(p \wedge \neg p = F\)
\(\neg q \wedge q = F\)
\(F \wedge F = F\)
Always false \(\Rightarrow\) contradiction.
Step 3: Final Answer
\[ \text{A contradiction} \]
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