Solution to 5.
5. Use a truth table to answer the following questions about the following 4 statements.
a) Are 1-3 consistent with 4?
b) Do any of 1-3 individually imply 4?
c) Do 1-3 jointly imply 4?
| |
|
|
|
|
|
|
|
|
|
| T | T | T | F | F | F | T | T | T | T |
| T | T | F | F | F | F | T | T | T | F |
| T | F | T | F | T | T | F | T | T | T |
| T | F | F | F | T | T | F | T | F | T |
| F | T | T | T | F | T | F | T | T | T |
| F | T | F | T | F | T | F | T | F | F |
| F | F | T | T | T | T | T | T | T | T |
| F | F | F | T | T | T | T | T | T | T |
a) Are 1-3 consistent with 4?
Yes. In the fifth row all
b) Do any of 1-3 individually imply 4?
1 does not imply 4, as can be seen by the sixth row in which 1 is T and 4 is F
2 does not imply 4, as can be seen by the second row in which 2 is T and 4 is F.
3 does not imply 4, as can be seen by the second row in which 2 is T and 4 is F.
c) Do 1-3 jointly imply 4?
Yes. There is no row on which all of 1-3 are T and 4 is F.