Mathematical Reasoning
Negation of Compound Statements
MMTS_Full_Test_19
Grade 12
Question:
Consider statements $P$: Sachin is a topper; $Q$: Sachin is sincere; $R$: Sachin is not demotivated. The negation of the statement 'If Sachin is sincere and he is not demotivated, then he is a topper' is
$P\to(Q\vee R)$
$(\sim P)\wedge(Q\wedge R)$
$P\to((\sim Q)\vee(\sim R))$
$P\to(Q\wedge R)$
Step-by-Step Solution
Key Concept: The statement is $(Q\wedge R)\to P$; its negation is $(Q\wedge R)\wedge(\sim P)=(\sim P)\wedge(Q\wedge R)$.
Statement: $(Q\wedge R)\to P$. Negation: $(Q\wedge R)\wedge\neg P = (\sim P)\wedge(Q\wedge R)$.
Correct Answer: B