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# The negation of the statement: ‘Getting above 95 percentage marks is a necessary condition for Hema to get the admission in a good college’.$a.{\text{ }}$Hema gets above 95 percentage marks but she does not get the admission in a good college.$b.{\text{ }}$Hema does not get above 95 percentage marks and she gets admission in a good college.$c.{\text{ }}$If Hema does not get above 95 percentage marks then she will not get the admission in a good college.$d.{\text{ }}$Hema does not get above 95 percentage marks or she gets admission in a good college.

Last updated date: 27th Mar 2023
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Hint: - Negation of $q \to p = \sim \left( {q \to p} \right)$

Let we suppose $p =$getting above 95 percentage marks.
And let, $q =$to get admission in a good college.
$\Rightarrow$Necessary condition according to question is
I.e. $p$ is a necessary condition for $q$.
$\Rightarrow$$q$ Depends on $p$
$\Rightarrow q \to p$
Now we have to find out the negation of above condition
$\Rightarrow$Negation of $q \to p = \sim \left( {q \to p} \right)$
By condition law
$\sim \left( {q \to p} \right) \equiv q \wedge \sim p$ ($q$ And negation of $p$)
By commutative law
$q \wedge \sim p \equiv \sim p \wedge q$ (Negation of $p$ and $q$)………………… (2)
$\Rightarrow$Negation of $p$ is$=$opposite of $p$
$=$Does not get above 95 percentage marks.

From equation (2)
Hema does not get above 95 percentage marks and she gets admission in a good college.
Hence, option (b) is correct.
Note: - In such types of questions the key concept we have to remember is that always remember the condition law, commutative law which is written above, and always remember that negation is a contradiction or denial of something, then after applying these properties we will get the required answer.