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