I'm having a bit of a hard time understanding logic and truth tables.
Determine whether the first formula logically implies the second or the second logically implies the first, or both, or neither.
~p -> (q ^ p) and (p ^ q) -> q (note: '->' means 'implies')
Firstly, I use the commutative law so (q ^ p) <=> (p ^ q) and hence ~p -> q.
Then I construct my truth table:
| p | q | ~p | ~p->q | | T | T | F | T | | T | F | F | T | | F | T | T | T | | F | F | T | F |
From the table how do I show that it logically implies or not?