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