Sets, Relations & Functions
Mathematical Reasoning
Grade None
Question:
<p>Negation of 'Paris is in France and London is in England' is</p>
<p>Paris is in England and London is in France</p>
<p>Paris is not in France or London is not in England</p>
<p>Paris is in England or London is in France</p>
<p>None of these</p>
Step-by-Step Solution
Key Concept: The negation of a conjunction (AND statement) is the disjunction (OR) of the negations of individual components, following De Morgan's Law: ¬(P ∧ Q) ≡ (¬P ∨ ¬Q).
<p><strong>Step 1:</strong> Identify the logical structure. The statement is: P ∧ Q, where</p><p>P: 'Paris is in France'</p><p>Q: 'London is in England'</p><p><strong>Step 2:</strong> Apply De Morgan's Law for negation of conjunction:</p><p>¬(P ∧ Q) ≡ (¬P ∨ ¬Q)</p><p><strong>Step 3:</strong> Substitute the negations:</p><p>¬P: 'Paris is not in France'</p><p>¬Q: 'London is not in England'</p><p><strong>Step 4:</strong> Write the final answer using OR (disjunction):</p><p>'Paris is not in France OR London is not in England'</p><p>∴ Answer: B</p>
Correct Answer: B