# 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.

Answer

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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.

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.

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