Sets, Relations & Functions
Mathematical Reasoning / Contrapositive
Grade 11
Question:
<p>Given statement is <em>p</em>: If it is raining, then I will not come. The contrapositive of statement <em>p</em> is:</p>
<p>If I will come, then it is not raining</p>
<p>If it is not raining, then I will come</p>
<p>If I will not come, then it is raining</p>
<p>If it is raining, then I will come</p>
Step-by-Step Solution
Key Concept: The contrapositive of (A → B) is (¬B → ¬A). You must negate both the hypothesis and conclusion, then reverse their order.
<p><strong>Step 1:</strong> Identify the original statement p in logical form.</p><p>Let R = 'it is raining' and C = 'I will come'</p><p>Statement p: R → ¬C (If it is raining, then I will not come)</p><p><strong>Step 2:</strong> Apply the contrapositive rule.</p><p>Contrapositive of (A → B) is (¬B → ¬A)</p><p>Contrapositive of (R → ¬C) is: ¬(¬C) → ¬R</p><p>Which simplifies to: C → ¬R</p><p><strong>Step 3:</strong> Write in words.</p><p>Contrapositive: 'If I come, then it is not raining'</p><p>∴ Answer: A</p>
Correct Answer: A