Sets, Relations & Functions
Mathematical Reasoning
Grade 11
Question:
<p>If \(p\) : 'Ram is tall' and \(q\) : 'Ram is intelligent', then the statement \(\sim p \vee q\) is</p>
<p>Ram is not tall or he is intelligent.</p>
<p>Ram is tall or he is intelligent.</p>
<p>Ram is not tall and he is intelligent.</p>
<p>Ram is not tall then he is intelligent.</p>
Step-by-Step Solution
Key Concept: The negation operator (~) flips the truth value of p, and the disjunction (∨) means 'or'. So ~p ∨ q translates to 'either Ram is not tall OR Ram is intelligent (or both)'.
<p><strong>Step 1:</strong> Identify the components: p = 'Ram is tall', q = 'Ram is intelligent'</p><p><strong>Step 2:</strong> Apply negation to p: ~p = 'Ram is not tall'</p><p><strong>Step 3:</strong> Apply disjunction (∨) which means 'or': ~p ∨ q represents the logical statement where at least one of the following is true:</p><ul><li>Ram is not tall, OR</li><li>Ram is intelligent, OR</li><li>Both</li></ul><p><strong>Step 4:</strong> The statement ~p ∨ q in words is: <strong>'Ram is not tall OR Ram is intelligent'</strong></p><p>∴ Answer: A</p>
Correct Answer: A