Question:
Consider the two statements \(P\): He is intelligent and \(Q\): He is strong. Then the symbolic form of the statement “It is not true that he is either intelligent or strong” is
Consider the two statements \(P\): He is intelligent and \(Q\): He is strong. Then the symbolic form of the statement “It is not true that he is either intelligent or strong” is
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Translate English statements carefully before applying logical rules.
Updated On: May 8, 2026
- \( \sim P \vee Q \)
- \( \sim P \vee \sim Q \)
- \( \sim P \wedge Q \)
- \( P \vee \sim Q \)
- \( \sim (P \vee Q) \)
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The Correct Option is
Solution and Explanation
Concept:
Translate English to logic:
• “Either \(P\) or \(Q\)” → \( P \vee Q \)
• “It is not true that” → negation
Step 1: Translate inner statement
“He is intelligent or strong” \[ P \vee Q \]
Step 2: Apply negation
“It is not true that…” \[ \sim (P \vee Q) \]
Step 3: Interpretation
This means: \[ \text{Neither intelligent nor strong} \]
Step 4: Equivalent form (optional)
Using De Morgan: \[ \sim P \wedge \sim Q \]
Step 5: Final Answer
\[ \boxed{\sim (P \vee Q)} \]
• “Either \(P\) or \(Q\)” → \( P \vee Q \)
• “It is not true that” → negation
Step 1: Translate inner statement
“He is intelligent or strong” \[ P \vee Q \]
Step 2: Apply negation
“It is not true that…” \[ \sim (P \vee Q) \]
Step 3: Interpretation
This means: \[ \text{Neither intelligent nor strong} \]
Step 4: Equivalent form (optional)
Using De Morgan: \[ \sim P \wedge \sim Q \]
Step 5: Final Answer
\[ \boxed{\sim (P \vee Q)} \]
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