Sets, Relations & Functions
Mathematical Reasoning / Contrapositive
Grade 11
Question:
<p>The contrapositive of the statement "I go to school if it does not rain" is:</p>
<p>If it rains, I do not go to school.</p>
<p>If I do not go to school, it rains.</p>
<p>(options cut off in image)</p>
<p>(options cut off in image)</p>
Step-by-Step Solution
Key Concept: The contrapositive of 'If P then Q' is 'If not Q then not P'. Here, identify P as 'it does not rain' and Q as 'I go to school', then negate and reverse both parts.
<p><strong>Step 1:</strong> Parse the original statement: 'I go to school if it does not rain'</p><p>This is: If (it does not rain) → Then (I go to school)</p><p>Let P = 'it does not rain' and Q = 'I go to school'</p><p><strong>Step 2:</strong> Apply contrapositive rule: ~Q → ~P</p><p>~Q = 'I do not go to school' (negation of Q)</p><p>~P = 'it rains' (negation of 'it does not rain')</p><p><strong>Step 3:</strong> Write the contrapositive: If I do not go to school → then it rains</p><p>Or equivalently: 'If I don't go to school, then it rains'</p><p>∴ Answer: B</p>
Correct Answer: B