Mister Exam

# Expression ¬(A∧B)∨¬(¬A∨¬B)∧¬(A∨B)

### The solution

You have entered [src]
(¬(a∧b))∨((¬(a∨b))∧(¬((¬a)∨(¬b))))
$$\left(\neg \left(a \vee b\right) \wedge \neg \left(\neg a \vee \neg b\right)\right) \vee \neg \left(a \wedge b\right)$$
Detail solution
$$\neg \left(a \wedge b\right) = \neg a \vee \neg b$$
$$\neg \left(a \vee b\right) = \neg a \wedge \neg b$$
$$\neg \left(\neg a \vee \neg b\right) = a \wedge b$$
$$\neg \left(a \vee b\right) \wedge \neg \left(\neg a \vee \neg b\right) = \text{False}$$
$$\left(\neg \left(a \vee b\right) \wedge \neg \left(\neg a \vee \neg b\right)\right) \vee \neg \left(a \wedge b\right) = \neg a \vee \neg b$$
Simplification [src]
$$\neg a \vee \neg b$$
(¬a)∨(¬b)
Truth table
+---+---+--------+
| a | b | result |
+===+===+========+
| 0 | 0 | 1      |
+---+---+--------+
| 0 | 1 | 1      |
+---+---+--------+
| 1 | 0 | 1      |
+---+---+--------+
| 1 | 1 | 0      |
+---+---+--------+
DNF [src]
$$\neg a \vee \neg b$$
(¬a)∨(¬b)
CNF [src]
$$\neg a \vee \neg b$$
(¬a)∨(¬b)
$$\neg a \vee \neg b$$
(¬a)∨(¬b)
$$\neg a \vee \neg b$$
(¬a)∨(¬b)