# Sufficient and necessary conditions

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

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

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.