Expression ¬((P∨¬Q)∧¬R)

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The solution

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¬((¬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]

Already transformed to DNF

$$r \vee \left(q \wedge \neg p\right)$$

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))

How to use it?

Identical expressions

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Expression ¬((P∨¬Q)∧¬R)

The solution