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JEE Main 202125 JulyEvening Shift
Exam
JEE Main
Year
2021
Date
25 July
Shift
Evening Shift
Subject
Mathematics
Chapter
Mathematical Reasoning

JEE Main 2021 · 25 July · Evening Shift · Mathematics · Mathematical Reasoning

Consider the statement "The match will be played only if the...

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

Options

  1. AThe match will not be played and weather is not good and ground is wet.
  2. BIf the match will not be played, then either weather is not good or ground is wet.
  3. CThe match will be played and weather is not good or ground is wet.
  4. DThe match will not be played or weather is good and ground is not wet.

Correct answer

C. The match will be played and weather is not good or ground is wet.

Step-by-step solution

Let p:p: weather is good
and q:q: ground is not wet

Given statement "The match will be played only if the weather is good and ground is not wet" can be written as (p∧q)\left(p ∧ q\right)

Now, negation of p∧qp ∧ q is  (p∧q)≡ p∨ q~ \left(p ∧ q\right) ≡ ~ p ∨ ~ q

which is equivalent to "The match will be played and weather is not good or ground is wet".

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