# Simplify $\neg p \lor \neg(q \land r)$

How can I simplify the following logical expression by using the laws of logic?

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

The answer given by my tutor is $q$ but it seems I can't figure out how to simplify it.

• The simplified version, as it stands, depends on all three variables. – астон вілла олоф мэллбэрг Oct 20 '16 at 13:09
• I am only able to simplify statement that have only 2 variable. However, when the expression has 3 variable, I am really lost. – Fafau Oct 20 '16 at 13:13
• No, but then you cannot simplify it further. The answer, as it stands, is $\overline{p} \vee \overline q \vee \overline r$, which can't be simplified further. – астон вілла олоф мэллбэрг Oct 20 '16 at 13:14
• Agree. That's how i get. I think the tutor has wrongly wrote the question – Fafau Oct 20 '16 at 13:19
• You may simplify it to $\neg(p\land q\land r)$. Looks kind of nice. – Michael Hoppe Oct 20 '16 at 13:23

$$\neg p\lor\neg(q\land r)\equiv \lnot p \lor (\lnot q \lor \lnot r) \tag {by DeMorgan's}$$
$$\equiv \lnot p \lor \lnot q \lor \lnot r\tag{parenthes not needed}$$