Sr Examen
Expresión (A⇒(D⇒C))⇒(A⇒(C⇒D))
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Solución
Ha introducido
[src]
(a⇒(d⇒c))⇒(a⇒(c⇒d))
$$\left(a \Rightarrow \left(d \Rightarrow c\right)\right) \Rightarrow \left(a \Rightarrow \left(c \Rightarrow d\right)\right)$$
Solución detallada
$$d \Rightarrow c = c \vee \neg d$$
$$a \Rightarrow \left(d \Rightarrow c\right) = c \vee \neg a \vee \neg d$$
$$c \Rightarrow d = d \vee \neg c$$
$$a \Rightarrow \left(c \Rightarrow d\right) = d \vee \neg a \vee \neg c$$
$$\left(a \Rightarrow \left(d \Rightarrow c\right)\right) \Rightarrow \left(a \Rightarrow \left(c \Rightarrow d\right)\right) = d \vee \neg a \vee \neg c$$
$$a \Rightarrow \left(d \Rightarrow c\right) = c \vee \neg a \vee \neg d$$
$$c \Rightarrow d = d \vee \neg c$$
$$a \Rightarrow \left(c \Rightarrow d\right) = d \vee \neg a \vee \neg c$$
$$\left(a \Rightarrow \left(d \Rightarrow c\right)\right) \Rightarrow \left(a \Rightarrow \left(c \Rightarrow d\right)\right) = d \vee \neg a \vee \neg c$$
Tabla de verdad
+---+---+---+--------+ | a | c | d | 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 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+