Sr Examen
Expresión Cv(¬C&B)&(C⇒B)⇒Av(¬A⇒C)
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
(c∨(b∧(¬c)∧(c⇒b)))⇒(a∨((¬a)⇒c))
$$\left(c \vee \left(b \wedge \left(c \Rightarrow b\right) \wedge \neg c\right)\right) \Rightarrow \left(a \vee \left(\neg a \Rightarrow c\right)\right)$$
Solución detallada
$$c \Rightarrow b = b \vee \neg c$$
$$b \wedge \left(c \Rightarrow b\right) \wedge \neg c = b \wedge \neg c$$
$$c \vee \left(b \wedge \left(c \Rightarrow b\right) \wedge \neg c\right) = b \vee c$$
$$\neg a \Rightarrow c = a \vee c$$
$$a \vee \left(\neg a \Rightarrow c\right) = a \vee c$$
$$\left(c \vee \left(b \wedge \left(c \Rightarrow b\right) \wedge \neg c\right)\right) \Rightarrow \left(a \vee \left(\neg a \Rightarrow c\right)\right) = a \vee c \vee \neg b$$
$$b \wedge \left(c \Rightarrow b\right) \wedge \neg c = b \wedge \neg c$$
$$c \vee \left(b \wedge \left(c \Rightarrow b\right) \wedge \neg c\right) = b \vee c$$
$$\neg a \Rightarrow c = a \vee c$$
$$a \vee \left(\neg a \Rightarrow c\right) = a \vee c$$
$$\left(c \vee \left(b \wedge \left(c \Rightarrow b\right) \wedge \neg c\right)\right) \Rightarrow \left(a \vee \left(\neg a \Rightarrow c\right)\right) = a \vee c \vee \neg b$$
Tabla de verdad
+---+---+---+--------+ | a | b | c | result | +===+===+===+========+ | 0 | 0 | 0 | 1 | +---+---+---+--------+ | 0 | 0 | 1 | 1 | +---+---+---+--------+ | 0 | 1 | 0 | 0 | +---+---+---+--------+ | 0 | 1 | 1 | 1 | +---+---+---+--------+ | 1 | 0 | 0 | 1 | +---+---+---+--------+ | 1 | 0 | 1 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+