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]
    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))
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