To keep our discussion as general as possible, we will adopt the following definitions of sufficient conditions and necessary conditions:
Feature F is a sufficient condition for feature G if and only if anything that has feature F also has feature G.
Feature F is a necessary condition for feature G if and only if anything that lacks feature F also lacks feature G.
These definitions are equivalent to those in the previous section, because, if anything that lacks feature F also lacks feature G, then anything that has feature G must also have feature F; and if anything that has feature G must also have feature F, then anything that lacks feature F also lacks feature G. It follows that feature F is a sufficient condition for feature G if and only if feature G is a nec- essary condition for feature F.
When F is sufficient for G, the relation between these features can be dia- grammed like this:
The inside circle represents the sufficient condition, because anything inside that inside circle must also be inside the outside circle. The outside circle repre- sents the necessary condition, for anything outside the outside circle must also be outside the inside circle.
These diagrams, along with the preceding definitions, should make it clear that something can be a sufficient condition for a feature without being a necessary condition for that feature, and vice versa.
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