Sr Examen
Expresión ¬(a⇒b)∧(¬c∨¬d)∨¬(a∨b)∧¬(c∧d)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
((¬(c∧d))∧(¬(a∨b)))∨((¬(a⇒b))∧((¬c)∨(¬d)))
$$\left(\neg \left(c \wedge d\right) \wedge \neg \left(a \vee b\right)\right) \vee \left(a \not\Rightarrow b \wedge \left(\neg c \vee \neg d\right)\right)$$
Solución detallada
$$\neg \left(c \wedge d\right) = \neg c \vee \neg d$$
$$\neg \left(a \vee b\right) = \neg a \wedge \neg b$$
$$\neg \left(c \wedge d\right) \wedge \neg \left(a \vee b\right) = \neg a \wedge \neg b \wedge \left(\neg c \vee \neg d\right)$$
$$a \Rightarrow b = b \vee \neg a$$
$$a \not\Rightarrow b = a \wedge \neg b$$
$$a \not\Rightarrow b \wedge \left(\neg c \vee \neg d\right) = a \wedge \neg b \wedge \left(\neg c \vee \neg d\right)$$
$$\left(\neg \left(c \wedge d\right) \wedge \neg \left(a \vee b\right)\right) \vee \left(a \not\Rightarrow b \wedge \left(\neg c \vee \neg d\right)\right) = \neg b \wedge \left(\neg c \vee \neg d\right)$$
$$\neg \left(a \vee b\right) = \neg a \wedge \neg b$$
$$\neg \left(c \wedge d\right) \wedge \neg \left(a \vee b\right) = \neg a \wedge \neg b \wedge \left(\neg c \vee \neg d\right)$$
$$a \Rightarrow b = b \vee \neg a$$
$$a \not\Rightarrow b = a \wedge \neg b$$
$$a \not\Rightarrow b \wedge \left(\neg c \vee \neg d\right) = a \wedge \neg b \wedge \left(\neg c \vee \neg d\right)$$
$$\left(\neg \left(c \wedge d\right) \wedge \neg \left(a \vee b\right)\right) \vee \left(a \not\Rightarrow b \wedge \left(\neg c \vee \neg d\right)\right) = \neg b \wedge \left(\neg c \vee \neg d\right)$$
Tabla de verdad
+---+---+---+---+--------+ | a | b | c | d | result | +===+===+===+===+========+ | 0 | 0 | 0 | 0 | 1 | +---+---+---+---+--------+ | 0 | 0 | 0 | 1 | 1 | +---+---+---+---+--------+ | 0 | 0 | 1 | 0 | 1 | +---+---+---+---+--------+ | 0 | 0 | 1 | 1 | 0 | +---+---+---+---+--------+ | 0 | 1 | 0 | 0 | 0 | +---+---+---+---+--------+ | 0 | 1 | 0 | 1 | 0 | +---+---+---+---+--------+ | 0 | 1 | 1 | 0 | 0 | +---+---+---+---+--------+ | 0 | 1 | 1 | 1 | 0 | +---+---+---+---+--------+ | 1 | 0 | 0 | 0 | 1 | +---+---+---+---+--------+ | 1 | 0 | 0 | 1 | 1 | +---+---+---+---+--------+ | 1 | 0 | 1 | 0 | 1 | +---+---+---+---+--------+ | 1 | 0 | 1 | 1 | 0 | +---+---+---+---+--------+ | 1 | 1 | 0 | 0 | 0 | +---+---+---+---+--------+ | 1 | 1 | 0 | 1 | 0 | +---+---+---+---+--------+ | 1 | 1 | 1 | 0 | 0 | +---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 0 | +---+---+---+---+--------+
FNDP
[src]
$$\left(\neg b \wedge \neg c\right) \vee \left(\neg b \wedge \neg d\right)$$
((¬b)∧(¬c))∨((¬b)∧(¬d))
FND
[src]
$$\left(\neg b \wedge \neg c\right) \vee \left(\neg b \wedge \neg d\right)$$
((¬b)∧(¬c))∨((¬b)∧(¬d))