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Mathematical Reasoning
hard
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
$((\sim P) \vee \sim Q) \wedge((\sim P) \vee R)$
B
$((\sim P ) \vee \sim Q ) \wedge((\sim P ) \vee \sim R )$
C
$(P \vee Q) \wedge((\sim P) \vee R)$
D
$(P \vee \sim Q) \wedge(P \vee \sim R)$
(JEE MAIN-2023)
Solution
$P \rightarrow(\sim Q \wedge R )$
$\sim P \vee(\sim Q \wedge R )$
$(\sim P \vee \sim Q ) \wedge(\sim P \vee R )$
Standard 11
Mathematics
