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