Question

 ^{Using the truth diagram, check whether the statement ~(p↑q) ↑(~p↓q) and ~ p are logically equivalent}

Answer 1

The truth table for the statements ~(p↑q) ↑(~p↓q) and ~p is given below:

| p | q | ~(p↑q) | ~p↓q | ~(p↑q) ↑(~p↓q) | ~p |
|---|---|---|---|---|---|
| T | T | F | T | T | F |
| T | F | T | F | F | F |
| F | T | T | T | T | T |
| F | F | T | T | T | T |

As we can see from the truth table, the two statements have the same truth values in all possible cases. Therefore, they are logically equivalent.