Question
Discrete math
Show that ~(p^q)and ~pv~q are logically equivalent
Show that ~(p^q)and ~pv~q are logically equivalent
Answers
GPT 3.5
To show that ~(p ^ q) and ~p v ~q are logically equivalent, we can use De Morgan's Laws:
De Morgan's Laws state that ~(p ^ q) is equivalent to ~p v ~q and ~(p v q) is equivalent to ~p ^ ~q.
So, we can rewrite ~(p ^ q) as ~p v ~q using De Morgan's Laws.
Therefore, ~(p ^ q) and ~p v ~q are logically equivalent.
De Morgan's Laws state that ~(p ^ q) is equivalent to ~p v ~q and ~(p v q) is equivalent to ~p ^ ~q.
So, we can rewrite ~(p ^ q) as ~p v ~q using De Morgan's Laws.
Therefore, ~(p ^ q) and ~p v ~q are logically equivalent.