Sets, Relations & Functions
Mathematical Logic - Negation
Grade 11
Question:
<p>The negation of the statement "If I become a teacher, then I will open a school", is:</p>
<p>I will become a teacher and I will not open a school.</p>
<p>Either I will not become a teacher or I will not open a school.</p>
<p>Neither I will become a teacher nor I will open a school.</p>
<p>I will not become a teacher or I will open a school.</p>
Step-by-Step Solution
Key Concept: The negation of a conditional statement 'If P then Q' is 'P and not Q', not 'If not P then not Q'. The contrapositive is logically equivalent to the original, but negation requires both the condition to hold AND the conclusion to fail.
<p><strong>Step 1:</strong> Identify the original statement structure.</p><p>Let P = 'I become a teacher'</p><p>Let Q = 'I will open a school'</p><p>Original statement: P → Q</p><p><strong>Step 2:</strong> Apply negation rule for conditional statements.</p><p>¬(P → Q) ≡ P ∧ ¬Q</p><p><strong>Step 3:</strong> Write the negation in words.</p><p>The negation is: 'I become a teacher AND I will not open a school'</p><p>or equivalently: 'I become a teacher but I will not open a school'</p><p>∴ Answer: A</p>
Correct Answer: A