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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?

Mauro ALLEGRANZA
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Aura
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1 Answers1

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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?

saulspatz
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  • Thank you for an answer. I am confused as to how p & q are chosen in both the statements. P: Indian team wins the match , Q: Selection committee selects an all rounder. The question says p is necessary for q, so q->p should be If selection committee selects and all rounder then Indian team wins the match? Still confused a bit why original answer is different. – Aura Mar 27 '20 at 10:13