Taken from elementary mathematics I am little confused as to conversion of below implications:
Q 1.) A necessary condition for Indian team to win a cricket match is that the selection committee selects an all rounder.
Solution: q is necessary for p p: Indian team wins a cricket match q: The selection committee selects an all rounder. if p then q "If the teams wins cricket match then selection committee selects an all rounder"
My Solution: "If the selection committee selects an all rounder then the team wins cricket match."
Q 2.) A sufficient condition for Tara to visit New Delhi is that she goes to the Rashtrapati Bhawan (a building in new delhi). p: Tara goes to the Rashtrapati Bhawan q: She visits New Delhi Solution: If Tara goes to Rashtrapati Bhawan, then she visits new Delhi.
My solution: "If Tara visits New Delhi, then she goes to Rashtrapati Bhawan".
Can anyone please guide me why my solutions are wrong in both the above cases? What am I missing in my logic?
You are confusing necessary and sufficient.
$p$ is necessary for $q$ means than $q$ can't hold unless $p$ does. ("$q$ needs $p$".) So if $q$ is true, then $p$ must be true. That is $q\rightarrow p$.
$p$ is sufficient for $q$ means that if $p$ holds then $q$ does. ("$p$ is enough for $q$".) So, if $p$ is true, so also is $q$. That is, $p\rightarrow q$.
EDIT
In reply to OP's comment.
The first statement says Q is necessary for P, not P is necessary for Q. The statement means that India can't win unless the committee selects an all-rounder, doesn't it?