Mister Exam

# Expression ¬((P∨¬Q)∧¬R)

### The solution

You have entered [src]
¬((¬r)∧(p∨(¬q)))
$$\neg \left(\neg r \wedge \left(p \vee \neg q\right)\right)$$
Detail solution
$$\neg \left(\neg r \wedge \left(p \vee \neg q\right)\right) = r \vee \left(q \wedge \neg p\right)$$
Simplification [src]
$$r \vee \left(q \wedge \neg p\right)$$
r∨(q∧(¬p))
Truth table
+---+---+---+--------+
| p | q | r | result |
+===+===+===+========+
| 0 | 0 | 0 | 0      |
+---+---+---+--------+
| 0 | 0 | 1 | 1      |
+---+---+---+--------+
| 0 | 1 | 0 | 1      |
+---+---+---+--------+
| 0 | 1 | 1 | 1      |
+---+---+---+--------+
| 1 | 0 | 0 | 0      |
+---+---+---+--------+
| 1 | 0 | 1 | 1      |
+---+---+---+--------+
| 1 | 1 | 0 | 0      |
+---+---+---+--------+
| 1 | 1 | 1 | 1      |
+---+---+---+--------+
DNF [src]
$$r \vee \left(q \wedge \neg p\right)$$
r∨(q∧(¬p))
CNF [src]
$$\left(q \vee r\right) \wedge \left(r \vee \neg p\right)$$
(q∨r)∧(r∨(¬p))
PDNF [src]
$$r \vee \left(q \wedge \neg p\right)$$
r∨(q∧(¬p))
PCNF [src]
$$\left(q \vee r\right) \wedge \left(r \vee \neg p\right)$$
(q∨r)∧(r∨(¬p))
To see a detailed solution - share to all your student friends
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share to all your student friends: