What's the differences between [NOT p OR NOT q] and [NOT (p OR q) ]

Question

I think these two statements are similar, can anyone tell me the differences?

Answer 1

Please take a look at the summary of Logic Operations we have, and the precedence of operations. Based on precedence of operation:

$\neg p \lor \neg q = (\neg p) \lor (\neg q)$

and if you look at rule 9 in the figure below, De Morgan's law, we have:

$\neg (p \lor q) = \neg p \land \neg q = (\neg p) \land (\neg q)$

 

Answer 2

p	q	not p	not q	not p or not q	p or q	not(p or q)
T	T	F	F	F	T	F
T	F	F	T	T	T	F
F	T	T	F	T	T	F
F	F	T	T	T	F	T

I write a truth table about the question,  you can find that [NOT p OR NOT q] and [NOT(p OR q)]are different.