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

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Question:

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:

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

  2. If the match will not be played, then either weather is not good or ground is wet.

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

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


Correct Option: , 3

Solution:

$\mathrm{p}:$ weather is food

$\mathrm{q}$ : ground is not wet

$\sim(p \wedge q) \equiv \sim p \vee \sim q$

$\equiv$ weather is not good or ground is wet

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