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]
    Already transformed to DNF
    $$\neg a \vee \neg b$$
    (¬a)∨(¬b)
    CNF [src]
    Already transformed to CNF
    $$\neg a \vee \neg b$$
    (¬a)∨(¬b)
    PCNF [src]
    $$\neg a \vee \neg b$$
    (¬a)∨(¬b)
    PDNF [src]
    $$\neg a \vee \neg b$$
    (¬a)∨(¬b)
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