Please take a look at the summary of Logic Operations we have, and the precedence of operations. Based on precedence of operation:
¬p∨¬q=(¬p)∨(¬q)
and if you look at rule 9 in the figure below, De Morgan's law, we have:
¬(p∨q)=¬p∧¬q=(¬p)∧(¬q)
I write a truth table about the question, you can find that [NOT p OR NOT q] and [NOT(p OR q)]are different.
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