Sr Examen
Expresión (a⇒b*¬c)*(c⇒b*a)*(b⇒c*a)
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Solución
Ha introducido
[src]
(b⇒(a∧c))∧(c⇒(a∧b))∧(a⇒(b∧(¬c)))
$$\left(a \Rightarrow \left(b \wedge \neg c\right)\right) \wedge \left(b \Rightarrow \left(a \wedge c\right)\right) \wedge \left(c \Rightarrow \left(a \wedge b\right)\right)$$
Solución detallada
$$b \Rightarrow \left(a \wedge c\right) = \left(a \wedge c\right) \vee \neg b$$
$$c \Rightarrow \left(a \wedge b\right) = \left(a \wedge b\right) \vee \neg c$$
$$a \Rightarrow \left(b \wedge \neg c\right) = \left(b \wedge \neg c\right) \vee \neg a$$
$$\left(a \Rightarrow \left(b \wedge \neg c\right)\right) \wedge \left(b \Rightarrow \left(a \wedge c\right)\right) \wedge \left(c \Rightarrow \left(a \wedge b\right)\right) = \neg a \wedge \neg b \wedge \neg c$$
$$c \Rightarrow \left(a \wedge b\right) = \left(a \wedge b\right) \vee \neg c$$
$$a \Rightarrow \left(b \wedge \neg c\right) = \left(b \wedge \neg c\right) \vee \neg a$$
$$\left(a \Rightarrow \left(b \wedge \neg c\right)\right) \wedge \left(b \Rightarrow \left(a \wedge c\right)\right) \wedge \left(c \Rightarrow \left(a \wedge b\right)\right) = \neg a \wedge \neg b \wedge \neg c$$
Tabla de verdad
+---+---+---+--------+ | a | b | c | result | +===+===+===+========+ | 0 | 0 | 0 | 1 | +---+---+---+--------+ | 0 | 0 | 1 | 0 | +---+---+---+--------+ | 0 | 1 | 0 | 0 | +---+---+---+--------+ | 0 | 1 | 1 | 0 | +---+---+---+--------+ | 1 | 0 | 0 | 0 | +---+---+---+--------+ | 1 | 0 | 1 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 0 | +---+---+---+--------+