Sr Examen
Expresión cbv!(ab→(!(bc)a=ab))→cav!a
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
((b∧c)∨(¬((a∧b)⇒((a∧b)⇔(a∧(¬(b∧c)))))))⇒((¬a)∨(a∧c))
$$\left(\left(b \wedge c\right) \vee \left(a \wedge b\right) \not\Rightarrow \left(\left(a \wedge b\right) ⇔ \left(a \wedge \neg \left(b \wedge c\right)\right)\right)\right) \Rightarrow \left(\left(a \wedge c\right) \vee \neg a\right)$$
Solución detallada
$$\neg \left(b \wedge c\right) = \neg b \vee \neg c$$
$$a \wedge \neg \left(b \wedge c\right) = a \wedge \left(\neg b \vee \neg c\right)$$
$$\left(a \wedge b\right) ⇔ \left(a \wedge \neg \left(b \wedge c\right)\right) = \left(b \wedge \neg c\right) \vee \neg a$$
$$\left(a \wedge b\right) \Rightarrow \left(\left(a \wedge b\right) ⇔ \left(a \wedge \neg \left(b \wedge c\right)\right)\right) = \neg a \vee \neg b \vee \neg c$$
$$\left(a \wedge b\right) \not\Rightarrow \left(\left(a \wedge b\right) ⇔ \left(a \wedge \neg \left(b \wedge c\right)\right)\right) = a \wedge b \wedge c$$
$$\left(b \wedge c\right) \vee \left(a \wedge b\right) \not\Rightarrow \left(\left(a \wedge b\right) ⇔ \left(a \wedge \neg \left(b \wedge c\right)\right)\right) = b \wedge c$$
$$\left(a \wedge c\right) \vee \neg a = c \vee \neg a$$
$$\left(\left(b \wedge c\right) \vee \left(a \wedge b\right) \not\Rightarrow \left(\left(a \wedge b\right) ⇔ \left(a \wedge \neg \left(b \wedge c\right)\right)\right)\right) \Rightarrow \left(\left(a \wedge c\right) \vee \neg a\right) = 1$$
$$a \wedge \neg \left(b \wedge c\right) = a \wedge \left(\neg b \vee \neg c\right)$$
$$\left(a \wedge b\right) ⇔ \left(a \wedge \neg \left(b \wedge c\right)\right) = \left(b \wedge \neg c\right) \vee \neg a$$
$$\left(a \wedge b\right) \Rightarrow \left(\left(a \wedge b\right) ⇔ \left(a \wedge \neg \left(b \wedge c\right)\right)\right) = \neg a \vee \neg b \vee \neg c$$
$$\left(a \wedge b\right) \not\Rightarrow \left(\left(a \wedge b\right) ⇔ \left(a \wedge \neg \left(b \wedge c\right)\right)\right) = a \wedge b \wedge c$$
$$\left(b \wedge c\right) \vee \left(a \wedge b\right) \not\Rightarrow \left(\left(a \wedge b\right) ⇔ \left(a \wedge \neg \left(b \wedge c\right)\right)\right) = b \wedge c$$
$$\left(a \wedge c\right) \vee \neg a = c \vee \neg a$$
$$\left(\left(b \wedge c\right) \vee \left(a \wedge b\right) \not\Rightarrow \left(\left(a \wedge b\right) ⇔ \left(a \wedge \neg \left(b \wedge c\right)\right)\right)\right) \Rightarrow \left(\left(a \wedge c\right) \vee \neg a\right) = 1$$
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 | 1 | +---+---+---+--------+