Solution to 1.
1. Use a truth table to decide each of the following (and explain how you determined each answer):
a) are the statements consistent?
b) does the first statement imply the second?
c) does the second imply the first?
d) are the statements equivalent?
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| T | T | F | T | F |
| T | F | F | T | F |
| F | T | T | F | T |
| F | F | T | T | F |
To make things easier to refer to, I have made the truth colum of statement one bold, and the column of statement two italic.
a) are the statements consistent?
No. There is no row in which both statements are T.
b) does the first statement imply the second?
No. It is possible for the first to be true and the second false. The first row is an instance of this.
c) does the second imply the first?
No. It is possible for the second to be true and the first false. The third row.
d) are the statements equivalent?
No. They do not have identical truth columns. In fact, their columns are contradictory.