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GO Classes DPP | GATE CS | Discrete Mathematics| Propositional Logic

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5 5 votes

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. $((\sim P) \vee \sim Q) \wedge((\sim P) \vee \sim R)$
  2. $(P \vee \sim Q) \wedge(P \vee \sim R)$
  3. $((\sim P) \vee \sim Q) \wedge((\sim P) \vee R)$
  4. $(P \vee Q) \wedge((\sim P) \vee R)$

6 Answers

1 1 vote

P: I have fever

Q: I will not take medicine

R: I will take rest

If I have fever, then i will take medicine and I will take rest

= If P, then ¬Q and R

= If P, then (¬Q ∧ R)

= P → (¬Q ∧ R)

= ¬P ∨ (¬Q ∧ R)

= (¬P ∨ ¬Q) ∧ (¬P ∨ R)    {Distributive laws}

 

Answer: C

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