For the given statement,identify the necessary and sufficient conditions.
$t:$ If you drive over $80 \, km/h$,then you will get a fine.
$t:$ If you drive over $80 \, km/h$,then you will get a fine.
(N/A) Let $p$ and $q$ denote the statements:
$p:$ You drive over $80 \, km/h$.
$q:$ You will get a fine.
The implication $p \implies q$ indicates that $p$ is a sufficient condition for $q$. That is,driving over $80 \, km/h$ is sufficient to get a fine.
Therefore,the sufficient condition is "driving over $80 \, km/h$".
Similarly,the implication $p \implies q$ indicates that $q$ is a necessary condition for $p$. That is,to drive over $80 \, km/h$,it is necessary to get a fine.
Therefore,the necessary condition is "getting a fine".
$p:$ You drive over $80 \, km/h$.
$q:$ You will get a fine.
The implication $p \implies q$ indicates that $p$ is a sufficient condition for $q$. That is,driving over $80 \, km/h$ is sufficient to get a fine.
Therefore,the sufficient condition is "driving over $80 \, km/h$".
Similarly,the implication $p \implies q$ indicates that $q$ is a necessary condition for $p$. That is,to drive over $80 \, km/h$,it is necessary to get a fine.
Therefore,the necessary condition is "getting a fine".
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