Conditional Propositions in English statements

          p -> q

1. if p then q.
2. When p, q.
3. q if p.
4. p only if q.
5. A neccessary condition for p is q.
   That is, when p is true, q must be true to make (p -> q) true.
6. A sufficient condition for q is p.
   That is, when q is true, p can be either true or false to make (p -> q) true.
   As long as q is true, (p->q) is always true no matter p is true or not.
   Therefore, p true is suffient.
p q p -> q message
T T T If p is true, q must be true. q is neccessary being true.
As long as q is true, p can be true or false. p is sufficient condition.
T F F
F T T As long as q is true, p can be true or false. p is sufficient condition.
F F T