Sufficient condition

A sufficient condition--call this 'Q'--for P is one such that if Q obtains, its obtaining is enough for P to also obtain. For example:

• Today is Thursday

is sufficient for

• Today is not Friday.

That is, today being Thursday means that today is also not Friday because it must not be Friday in order for it to be Thursday (or any other day of the week). In other words, since we know that today is Thursday, we know enough information to also know that today is not Friday.

A sufficient condition is to be contrasted with a necessary condition. A necessary condition--call this 'P'--for Q is one such that if P obtains, its obtaining is not enough by itself for Q to also obtain. For example:

• Today is not Friday

is necessary for

• Today is Thursday.

That is, today being not Friday is one (but not all) of the conditions that must obtain in order for today to be Thursday. In other words, if we know that today is not Friday, this is one of the many things we need to know for it to be Thursday: it must also not be Saturday, not be Sunday, not be Monday, not be Tuesday, and not be Wednesday. If we know it is not any of these days (Friday-Wednesday), then and only then can we know that today is Thursday.

The two conditions are related. P is a necessary condition for Q just in case Q is a sufficient condition for P. So, in our example 'Today is not Friday'=P and 'Today is Thursday'=Q. If we know that Q is true, that is enough to know that P is also true; but if we know that P is true, that is by itself not enough to know that Q is true.

• See also Necessary and sufficient
• See also Gettier problem