Solution to 3.
3. Use a truth table to answer the following questions about the following 3 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 | T | T | T |
| T | T | T | F | F | T |
| T | T | F | T | T | F |
| T | T | F | F | F | F |
| T | F | T | T | T | T |
| T | F | T | F | T | T |
| T | F | F | T | T | F |
| T | F | F | F | T | F |
| F | T | T | T | T | T |
| F | T | T | F | F | T |
| F | T | F | T | T | T |
| F | T | F | F | F | T |
| F | F | T | T | T | T |
| F | F | T | F | T | T |
| F | F | F | T | T | T |
| F | F | F | F | T | T |
a) Are 1-2 consistent with 3?
Yes. It is possible for all to be true at once. Row 1 is an example.
b) Do any of 1-2 individually imply 3?
1 does not imply 3, as can be seen by row 3 in which 1 is T and 3 is F.
2 does not imply 3, as can be seen by the same row, in which 2 is T and 3 is F.
c) Do 1-2 jointly imply 3?
No. There are rows in which 1 and 2 are both T, but 3 is F. Row 3 is an example.