Sr Examen
Expresión (A⇔B*C)⇒((B⇔A*D)+C)
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Solución
Ha introducido
[src]
(a⇔(b∧c))⇒(c∨(b⇔(a∧d)))
$$\left(a ⇔ \left(b \wedge c\right)\right) \Rightarrow \left(c \vee \left(b ⇔ \left(a \wedge d\right)\right)\right)$$
Solución detallada
$$a ⇔ \left(b \wedge c\right) = \left(\neg a \wedge \neg b\right) \vee \left(\neg a \wedge \neg c\right) \vee \left(a \wedge b \wedge c\right)$$
$$b ⇔ \left(a \wedge d\right) = \left(\neg a \wedge \neg b\right) \vee \left(\neg b \wedge \neg d\right) \vee \left(a \wedge b \wedge d\right)$$
$$c \vee \left(b ⇔ \left(a \wedge d\right)\right) = c \vee \left(\neg a \wedge \neg b\right) \vee \left(\neg b \wedge \neg d\right) \vee \left(a \wedge b \wedge d\right)$$
$$\left(a ⇔ \left(b \wedge c\right)\right) \Rightarrow \left(c \vee \left(b ⇔ \left(a \wedge d\right)\right)\right) = a \vee c \vee \neg b$$
$$b ⇔ \left(a \wedge d\right) = \left(\neg a \wedge \neg b\right) \vee \left(\neg b \wedge \neg d\right) \vee \left(a \wedge b \wedge d\right)$$
$$c \vee \left(b ⇔ \left(a \wedge d\right)\right) = c \vee \left(\neg a \wedge \neg b\right) \vee \left(\neg b \wedge \neg d\right) \vee \left(a \wedge b \wedge d\right)$$
$$\left(a ⇔ \left(b \wedge c\right)\right) \Rightarrow \left(c \vee \left(b ⇔ \left(a \wedge d\right)\right)\right) = a \vee c \vee \neg b$$
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 | 1 | +---+---+---+---+--------+ | 0 | 1 | 0 | 0 | 0 | +---+---+---+---+--------+ | 0 | 1 | 0 | 1 | 0 | +---+---+---+---+--------+ | 0 | 1 | 1 | 0 | 1 | +---+---+---+---+--------+ | 0 | 1 | 1 | 1 | 1 | +---+---+---+---+--------+ | 1 | 0 | 0 | 0 | 1 | +---+---+---+---+--------+ | 1 | 0 | 0 | 1 | 1 | +---+---+---+---+--------+ | 1 | 0 | 1 | 0 | 1 | +---+---+---+---+--------+ | 1 | 0 | 1 | 1 | 1 | +---+---+---+---+--------+ | 1 | 1 | 0 | 0 | 1 | +---+---+---+---+--------+ | 1 | 1 | 0 | 1 | 1 | +---+---+---+---+--------+ | 1 | 1 | 1 | 0 | 1 | +---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 1 | +---+---+---+---+--------+