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:

• A. $(P \vee Q) \wedge((\sim P) \vee R)$
• B. $(P \vee \sim Q) \wedge(P \vee \sim R)$
• C. $((\sim P) \vee \sim Q) \wedge((\sim P) \vee \sim R)$
• D. $((\sim P) \vee \sim Q)\wedge((\sim P) \vee R)$

Answer 1

Answer: (D)

$((\sim P) \vee \sim Q)\wedge((\sim P) \vee R)$

Answer 2

P→(∼Q∧R)
∼P∨(−Q∧R)
(−P∨∼Q)∧(−P∨R)
So, the correct answer is (D) : $((\sim P) \vee \sim Q) \vee((\sim P) \vee R)$