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Expresión CA∨¬(CAB→(¬BA⇔CB))⇔CA∨B¬A
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Solución
Ha introducido
[src]
((a∧c)∨(b∧(¬a)))⇔((a∧c)∨(¬((a∧b∧c)⇒((b∧c)⇔(a∧(¬b))))))
$$\left(\left(a \wedge c\right) \vee \left(b \wedge \neg a\right)\right) ⇔ \left(\left(a \wedge c\right) \vee \left(a \wedge b \wedge c\right) \not\Rightarrow \left(\left(a \wedge \neg b\right) ⇔ \left(b \wedge c\right)\right)\right)$$
Solución detallada
$$\left(a \wedge \neg b\right) ⇔ \left(b \wedge c\right) = \left(b \wedge \neg c\right) \vee \left(\neg a \wedge \neg b\right)$$
$$\left(a \wedge b \wedge c\right) \Rightarrow \left(\left(a \wedge \neg b\right) ⇔ \left(b \wedge c\right)\right) = \neg a \vee \neg b \vee \neg c$$
$$\left(a \wedge b \wedge c\right) \not\Rightarrow \left(\left(a \wedge \neg b\right) ⇔ \left(b \wedge c\right)\right) = a \wedge b \wedge c$$
$$\left(a \wedge c\right) \vee \left(a \wedge b \wedge c\right) \not\Rightarrow \left(\left(a \wedge \neg b\right) ⇔ \left(b \wedge c\right)\right) = a \wedge c$$
$$\left(\left(a \wedge c\right) \vee \left(b \wedge \neg a\right)\right) ⇔ \left(\left(a \wedge c\right) \vee \left(a \wedge b \wedge c\right) \not\Rightarrow \left(\left(a \wedge \neg b\right) ⇔ \left(b \wedge c\right)\right)\right) = a \vee \neg b$$
$$\left(a \wedge b \wedge c\right) \Rightarrow \left(\left(a \wedge \neg b\right) ⇔ \left(b \wedge c\right)\right) = \neg a \vee \neg b \vee \neg c$$
$$\left(a \wedge b \wedge c\right) \not\Rightarrow \left(\left(a \wedge \neg b\right) ⇔ \left(b \wedge c\right)\right) = a \wedge b \wedge c$$
$$\left(a \wedge c\right) \vee \left(a \wedge b \wedge c\right) \not\Rightarrow \left(\left(a \wedge \neg b\right) ⇔ \left(b \wedge c\right)\right) = a \wedge c$$
$$\left(\left(a \wedge c\right) \vee \left(b \wedge \neg a\right)\right) ⇔ \left(\left(a \wedge c\right) \vee \left(a \wedge b \wedge c\right) \not\Rightarrow \left(\left(a \wedge \neg b\right) ⇔ \left(b \wedge c\right)\right)\right) = a \vee \neg b$$
Tabla de verdad
+---+---+---+--------+ | a | b | c | result | +===+===+===+========+ | 0 | 0 | 0 | 1 | +---+---+---+--------+ | 0 | 0 | 1 | 1 | +---+---+---+--------+ | 0 | 1 | 0 | 0 | +---+---+---+--------+ | 0 | 1 | 1 | 0 | +---+---+---+--------+ | 1 | 0 | 0 | 1 | +---+---+---+--------+ | 1 | 0 | 1 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+