Question

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 1

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.