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Is it correct to say that sufficiency and necessity of a condition is like saying "if and only if"?

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    $\begingroup$ Yes, the two are equivalent. $\endgroup$ – Asier Calbet Aug 30 '14 at 22:17
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    $\begingroup$ Yes it is. $P\Rightarrow Q$ is '$P$ is sufficient for $Q$'. And $Q\Rightarrow P$ is '$P$ is necessary for $Q$'. $\endgroup$ – paw88789 Aug 30 '14 at 22:17
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Yes.

My knowing the combination to open this vault is a necessary condition to my finding $1 million inside it.

I will find $1 million inside the vault only if I know the combination.

The presence of $1 million in the middle of the vault that I open every morning is a sufficient condition for my finding it, since it's so conspicuous. I can't miss it.

I will find $1 million there if it is there.

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