Necessity Condition in Implication ?

[22990atinesh]

P -> Q

P	Q	P->Q
T	T	  T
T	F	  F
F	T	  T
F	F	  T

I understand the condition "P is sufficient for Q". But I'm not getting the meaning of why "Q is necessary for P". What does this signifies, Please explain ..

 

[Stephen Tashi]

. But I'm not getting the meaning of why "Q is necessary for P".

Is this a question about interpreting English?

One way to rephrase "Q is necessary for P" is to say "If Q is false then P must be false" or " not-Q implies not-P".

Thinking of P and Q as events you could rephrase "Q is necessary for P" as "If P happened then Q must also have happened" or "If Q doesn't happen then P can't happen".