Consider the following statements:P: I have f | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the statements be:$P$: $I$ have fever$Q$: $I$ will take medicine$R$: $I$ will take restThe given statement is: "If $I$ have fever,then $I$ wil

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) Let the statements be:$P$: $I$ have fever$Q$: $I$ will take medicine$R$: $I$ will take restThe given statement is: "If $I$ have fever,then $I$ will take medicine and $I$ will take rest".This can be written as: $P \rightarrow (Q \wedge R)$.Using the logical equivalence $A \rightarrow B \equiv \sim A \vee B$:$P \rightarrow (Q \wedge R) \equiv \sim P \vee (Q \wedge R)$.Using the distributive law $A \vee (B \wedge C) \equiv (A \vee B) \wedge (A \vee C)$:$\sim P \vee (Q \wedge R) \equiv (\sim P \vee Q) \wedge (\sim P \vee R)$.Wait,the original question statement is "$I$ will not take medicine" for $Q$. Let's re-evaluate.If $Q$ is "$I$ will take medicine",then "$I$ will not take medicine" is $\sim Q$.The statement is $P \rightarrow (\sim Q \wedge R)$.Equivalent to $\sim P \vee (\sim Q \wedge R)$.Applying distributive law: $(\sim P \vee \sim Q) \wedge (\sim P \vee R)$.

Consider the following statements:
$P$: $I$ have fever
$Q$: $I$ will 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:

Similar Questions

Which of the following sentences are statements? Give reasons for your answer.
The sum of all interior angles of a triangle is $180^{\circ}.$

Consider the statement "The match will be played only if the weather is good and the ground is not wet". Select the correct negation from the following:

For each of the following statements,determine whether an inclusive "Or" or exclusive "Or" is used. Give reasons for your answer.
The school is closed if it is a holiday or a Sunday.

Check whether the following pair of statements are negation of each other. Give reasons for your answer.
$I$: There exists real numbers $x$ and $y$ for which $x+y=y+x.$
$II$: For all real numbers $x$ and $y$,$x+y \neq y+x.$

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Consider the following statements:$P$: $I$ have fever$Q$: $I$ will take medicine$R$: $I$ will take restThe statement "If $I$ have fever,then $I$ will take medicine and $I$ will take rest" is equivalent to: