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put this solution on YOUR website!To construct the truth table for ~q --> (~q ^ p), let's first break it up:
First, let's make a truth table for ~q:
Note: just write the opposite of q for every entry
Now, let's make a table for ~q ^ p (simply use the "and" operator for columns ~q and p):
| p | q | ~q | ~q ^ p |
| T | T | F | F |
| T | F | T | T |
| F | T | F | F |
| F | F | T | F |
Note: ~q ^ p is only true when both ~q and p are true. Otherwise, it's false.
Finally, make a table for ~q --> (~q ^ p):
| p | q | ~q | ~q ^ p | ~q --> (~q ^ p) |
| T | T | F | F | T |
| T | F | T | T | T |
| F | T | F | F | T |
| F | F | T | F | F |
Recall that p -> q is only false when p is true and q is false. Otherwise, it is true.
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