JEE Main · 2023 · 30 Jan 2023 · Shift 2 · Mathematical Reasoning *

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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) $((\sim P) \lor \sim Q) \land ((\sim P) \lor R)$ ✓ Correct
(B) $((\sim P) \lor \sim Q) \land ((\sim P) \lor \sim R)$
(C) $(P \lor Q) \land ((\sim P) \lor R)$
(D) $(P \lor \sim Q) \land (P \lor \sim R)$

Answer: (A)

Solution

Because

Q

stands for ``I will not take medicine,'' taking medicine is

\sim Q

, so the statement reads

P \to (\sim Q \land R)

. Using

P \to X \equiv \sim P \lor X

and then distributing,

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

. The equivalent compound statement is

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

JEE Main · 2023 · 30 Jan 2023 · Shift 2 · Single correct option

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JEE Main · 2023 · 30 Jan 2023 · Shift 2 · Mathematical Reasoning *

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