Conditions

Necessary condition: where p and q are statements, p is a necessary condition for q if q cannot be true unless p is true; it is impossible for q to be true and p to be false; if p is a necessary condition for q, then the conditional “if q, then p” is true.
Sufficient condition: where p and q are statements, p is a sufficient condition for q if p’s truth guarantees the truth of q; it is impossible for p to be true and q to be false; if p is a sufficient condition for q, then the conditional “if p, then q” is true.

Note:  p is a necessary condition for q if and only if q is a sufficient condition for p.  Let us see why this is the case.  For example, take the following two statements: p- Jenny is from Newark, q- Jenny is from New Jersey.  From the definition of a necessary condition, we find that q is necessary for p (that is, it is impossible for p to be true and q to be false), making p sufficient for q (that is, p’s truth guarantees the truth of q).  

VII. Practice Exercises