Sr Examen
Expresión av¬(b&¬c)v¬(a⇒¬(¬b&c))
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Solución
Ha introducido
[src]
a∨(¬(b∧(¬c)))∨(¬(a⇒(¬(c∧(¬b)))))
$$a \vee \neg \left(b \wedge \neg c\right) \vee a \not\Rightarrow \neg \left(c \wedge \neg b\right)$$
Solución detallada
$$\neg \left(b \wedge \neg c\right) = c \vee \neg b$$
$$\neg \left(c \wedge \neg b\right) = b \vee \neg c$$
$$a \Rightarrow \neg \left(c \wedge \neg b\right) = b \vee \neg a \vee \neg c$$
$$a \not\Rightarrow \neg \left(c \wedge \neg b\right) = a \wedge c \wedge \neg b$$
$$a \vee \neg \left(b \wedge \neg c\right) \vee a \not\Rightarrow \neg \left(c \wedge \neg b\right) = a \vee c \vee \neg b$$
$$\neg \left(c \wedge \neg b\right) = b \vee \neg c$$
$$a \Rightarrow \neg \left(c \wedge \neg b\right) = b \vee \neg a \vee \neg c$$
$$a \not\Rightarrow \neg \left(c \wedge \neg b\right) = a \wedge c \wedge \neg b$$
$$a \vee \neg \left(b \wedge \neg c\right) \vee a \not\Rightarrow \neg \left(c \wedge \neg b\right) = a \vee c \vee \neg b$$
Tabla de verdad
+---+---+---+--------+ | a | b | c | result | +===+===+===+========+ | 0 | 0 | 0 | 1 | +---+---+---+--------+ | 0 | 0 | 1 | 1 | +---+---+---+--------+ | 0 | 1 | 0 | 0 | +---+---+---+--------+ | 0 | 1 | 1 | 1 | +---+---+---+--------+ | 1 | 0 | 0 | 1 | +---+---+---+--------+ | 1 | 0 | 1 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+