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JEE Main 202330 JanuaryEvening Shift
Exam
JEE Main
Year
2023
Date
30 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Mathematical Reasoning

JEE Main 2023 · 30 January · Evening Shift · Mathematics · Mathematical Reasoning

Consider the following statements: P : I have fever Q : I will not...

Consider the following statements:
PP : I have fever
QQ : I will not take medicine
RR : I will take rest
The statement "If I have fever, then I will take medicine and I will take rest" is equivalent to:

Options

  1. A(( P)∨ Q)∧(( P)∨R)\left(\left(~ P\right) ∨ ~ Q\right) ∧ \left(\left(~ P\right) ∨ R\right)
  2. B(( P)∨−Q)∧(( P)∨ R)\left(\left(~ P\right) ∨ - Q\right) ∧ \left(\left(~ P\right) ∨ ~ R\right)
  3. C(P∨Q)∧(( P)∨R)\left(P ∨ Q\right) ∧ \left(\left(~ P\right) ∨ R\right)
  4. D(P∨ Q)∧(P∨ R)\left(P ∨ ~ Q\right) ∧ \left(P ∨ ~ R\right)

Correct answer

A. (( P)∨ Q)∧(( P)∨R)\left(\left(~ P\right) ∨ ~ Q\right) ∧ \left(\left(~ P\right) ∨ R\right)

Step-by-step solution

We know the conditional statement:

{ifA,thenB}is given byA→B\left\{\text{if}A, \text{then}B\right\}\text{is given by}A \to B

So the given statements If I have fever, then I will take medicine and I will take rest can be written as,

P→( Q∧R)P \to \left(~ Q ∧ R\right)

≡ P∨( Q∧R)≡ ~ P ∨ \left(~ Q ∧ R\right)

≡(( P)∨ Q)∧(( P)∨R)≡ \left(\left(~ P\right) ∨ ~ Q\right) ∧ \left(\left(~ P\right) ∨ R\right)

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