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:

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 ∨ Q) ∧((∼ P) ∨ R) (B) (P ∨ ∼ Q) ∧(P ∨ ∼ R) (C) ((∼ P) ∨ ∼ Q) ∧((∼ P) ∨ ∼ R) (D) ((∼ P) ∨ ∼ Q) ∧((∼ P) ∨ R)

Tardigrade Admin · Accepted Answer

P arrow(∼ Q ∧ R) ∼ P ∨(-Q ∧ R) (-P ∨ ∼ Q) ∧(-P ∨ R)

Q. 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:

$(P \lor Q) \land ((\sim P) \lor R)$

$(P \lor \sim Q) \land (P \lor \sim R)$

$((\sim P) \lor \sim Q) \land ((\sim P) \lor \sim R)$

$((\sim P) \lor \sim Q) \land ((\sim P) \lor R)$

$P \to (\sim Q \land R)$
$\sim P \lor (- Q \land R)$
$(- P \lor \sim Q) \land (- P \lor R)$

Q. 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:

(P∨Q)∧((∼P)∨R)

(P∨∼Q)∧(P∨∼R)

((∼P)∨∼Q)∧((∼P)∨∼R)

((∼P)∨∼Q)∧((∼P)∨R)