(i) The compound statement ‘if p then q’ is implication of p and It is denoted by p → q or p ⇒ q. (read : p implication q)
Rule:
| p |
q |
p → q |
| T |
T |
T |
| T |
F |
F |
| F |
T |
T |
| F |
F |
T |
Note: If ‘p’ and then ‘q’ is small following:
- p ⇒ q (i.e., p implies q)
- p is sufficient condition for q
- p only if q
- q is necessary condition for p
- ~q implies ~p (i.e., ~q ⇒ ~p)
- The compound statement ‘p if and only if q’ is double implication of p and It is denoted by p ⇔ q (read: p double implication q)
- Rule:
| p |
q |
p ⇔ q |
| T |
T |
T |
| T |
F |
F |
| F |
T |
F |
| F |
F |
T |
Note: ‘p if and only if q’ is same as the following.
- p ⇔ q
- p if and only if q
- q if and only if p
- p is necessary and sufficient condition for q and vice-versa
