Discrete math

Question

Show that ~(p^q)and ~pv~q are logically equivalent

Answer 1

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.