|
Properties of Statements
| Q. Explain the following properties of statements |
| Ans.
Satisfiable: A statement is satisfiable if there
is some interpretation for which is true.
Contradiction: A sentence is contradictory (unsatisfiable)
if there is no interpretation for which its is true.
Valid: A sentence is valid if it is true for every
interpretation. Valid sentences are also called tautologies.
Equivalence: Two sentences are equivalent if they
have the same truth value under every interpretation.
|
Q. Determine for each of the following sentence, whether it
is satisfiable, contradictory or valid: (Dec. 01)
- (P & Q) Ú ~P
Ú ~Q
- (P Ú Q) à
(P & Q)
- P à Q à
~P
i.
| P |
Q |
~P |
~Q |
P & Q |
~P Ú
~Q |
(P & Q) Ú
~P Ú ~Q
|
| T |
T |
F |
F |
T |
F |
T |
| T |
F |
F |
T |
F |
T |
T |
| F |
T |
T |
F |
F |
T |
T |
| F |
F |
T |
T |
F |
T |
T |
The statement is valid because it is true for every interpretation.
ii.
| P |
Q |
P Ú
Q |
P & Q |
(P Ú
Q) à (P & Q) |
| T |
T |
T |
T |
T |
| T |
F |
T |
F |
F |
| F |
T |
T |
F |
F |
| F |
F |
F |
F |
T |
The statement is satisfiable.
iii.
| P |
Q |
~P |
~Q |
P à
Q |
P à
Q à ~P |
| T |
T |
F |
F |
T |
F |
| T |
F |
F |
T |
F |
T |
| F |
T |
T |
F |
T |
T |
| F |
F |
T |
T |
T |
T |
The statement is satisfiable.
|
AI
Contents
