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 |
|
if and only if
p |
q |
p -> q
q if p |
q -> p
q only if p |
(p -> q) and (q -> p)
q if and only if p |
| T |
T |
T |
T |
T |
| T |
F |
F |
T |
F |
| F |
T |
T |
F |
F |
| F |
F |
T |
T |
T |