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 |