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 :
Show Hint
- The match will not be played and weather is not good and ground is wet.
- If the match will not be played, then either weather is not good or ground is wet.
- The match will be played and weather is not good or ground is wet.
- The match will not be played or weather is good and ground is not wet.
The Correct Option is C
Solution and Explanation
\(\sim(p\to q)\equiv p\wedge\sim q\).
\(\sim q=\sim(\text{good}\wedge\text{not wet})=\text{not good}\vee\text{wet}\).
So the negation is: the match will be played and (the weather is not good or the ground is wet).
Answer: (3) The match will be played and weather is not good or ground is wet.
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