Question:
\((\sim p \wedge q)\) is logically equivalent to
\((\sim p \wedge q)\) is logically equivalent to
Show Hint
Use \(A \rightarrow B \equiv \sim A \vee B\) and De Morgan's laws.
Updated On: Apr 23, 2026
- \(p \rightarrow q\)
- \(q \rightarrow p\)
- \(\sim (p \rightarrow q)\)
- \(\sim (q \rightarrow p)\)
Show Solution
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The Correct Option is D
Solution and Explanation
Step 1: Formula / Definition}
\[ q \rightarrow p \equiv \sim q \vee p \]
Step 2: Calculation / Simplification}
\(\sim (q \rightarrow p) = \sim (\sim q \vee p) = q \wedge \sim p = \sim p \wedge q\)
\(\therefore \sim p \wedge q \equiv \sim (q \rightarrow p)\)
Step 3: Final Answer
\[ \sim (q \rightarrow p) \]
\[ q \rightarrow p \equiv \sim q \vee p \]
Step 2: Calculation / Simplification}
\(\sim (q \rightarrow p) = \sim (\sim q \vee p) = q \wedge \sim p = \sim p \wedge q\)
\(\therefore \sim p \wedge q \equiv \sim (q \rightarrow p)\)
Step 3: Final Answer
\[ \sim (q \rightarrow p) \]
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