Mathematical Reasoning
Symbolic Logic / English to Logic
nta_pyq_2023_jan
Grade 11
Question:
Consider the following statements: P: I have fever; Q: I will not take medicine; R: I will take rest. The statement "If I have fever, then I will take medicine and I will take rest" is equivalent to:
1. $(\sim P) \vee \sim Q) \wedge ((\sim P) \vee R)$
2. $(\sim P) \vee \sim Q) \wedge ((\sim P) \vee \sim R)$
3. $(P \vee Q) \wedge ((\sim P) \vee R)$
4. $(P \vee \sim Q) \wedge (P \vee \sim R)$
Step-by-Step Solution
Key Concept: "I will take medicine" is $\sim Q$; statement is $P \Rightarrow (\sim Q \wedge R) \equiv (\sim P\vee\sim Q)\wedge(\sim P\vee R)$.
$P\Rightarrow(\sim Q\wedge R)=\sim P\vee(\sim Q\wedge R)=(\sim P\vee\sim Q)\wedge(\sim P\vee R)$. Option (1).
Correct Answer: 1