Mathematical Reasoning
Mathematical Reasoning
nta_abhyas_2025
Grade 11
Question:
If $p$: A man is happy and $q$: A man is rich are two statements, then the statement, "If a man is not happy, then he is not rich" can be written using logical operators as
¬ p → ¬ q
¬ q → p
¬ q → ¬ p
q → ¬ p
Step-by-Step Solution
Key Concept: Direct translation of conditional statements using logical notation: 'If A then B' becomes $A \to B$.
The statement 'If man is not happy, then he is not rich' directly translates the negation of $p$ (not happy) as the antecedent and the negation of $q$ (not rich) as the consequent, giving $\neg p \to \neg q$. This is the contrapositive relationship to the original statement.
Correct Answer: F