Mister Exam
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How to use it?
- Expression:
- ¬(A∧B)∨¬(¬A∨¬B)∧¬(A∨B)
- (P⊕Q)∧((P→R)∨(Q→S))
- (p⇒(q⇒r))⇒((p⇒q)⇒(q⇒r))
- [(𝑝∨𝑞)∧(𝑝→𝑟)∧(𝑞→𝑟)]→𝑟
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Identical expressions
- ¬(A∧B)∨¬(¬A∨¬B)∧¬(A∨B)
- ¬A∧B∨¬¬A∨¬B∧¬A∨B
Expression ¬(A∧B)∨¬(¬A∨¬B)∧¬(A∨B)
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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
$$\neg \left(a \wedge b\right) = \neg a \vee \neg b$$
$$\neg \left(a \vee b\right) = \neg a \wedge \neg b$$
$$\neg \left(\neg a \vee \neg b\right) = a \wedge b$$
$$\neg \left(a \vee b\right) \wedge \neg \left(\neg a \vee \neg b\right) = \text{False}$$
$$\left(\neg \left(a \vee b\right) \wedge \neg \left(\neg a \vee \neg b\right)\right) \vee \neg \left(a \wedge b\right) = \neg a \vee \neg b$$
$$\neg \left(a \vee b\right) = \neg a \wedge \neg b$$
$$\neg \left(\neg a \vee \neg b\right) = a \wedge b$$
$$\neg \left(a \vee b\right) \wedge \neg \left(\neg a \vee \neg b\right) = \text{False}$$
$$\left(\neg \left(a \vee b\right) \wedge \neg \left(\neg a \vee \neg b\right)\right) \vee \neg \left(a \wedge b\right) = \neg a \vee \neg b$$
Truth table
+---+---+--------+ | a | b | result | +===+===+========+ | 0 | 0 | 1 | +---+---+--------+ | 0 | 1 | 1 | +---+---+--------+ | 1 | 0 | 1 | +---+---+--------+ | 1 | 1 | 0 | +---+---+--------+