Sr Examen
Expresión (a->b)->((b->c)->(avb->c))
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Solución
Ha introducido
[src]
(a⇒b)⇒((b⇒c)⇒((a∨b)⇒c))
$$\left(a \Rightarrow b\right) \Rightarrow \left(\left(b \Rightarrow c\right) \Rightarrow \left(\left(a \vee b\right) \Rightarrow c\right)\right)$$
Solución detallada
$$a \Rightarrow b = b \vee \neg a$$
$$b \Rightarrow c = c \vee \neg b$$
$$\left(a \vee b\right) \Rightarrow c = c \vee \left(\neg a \wedge \neg b\right)$$
$$\left(b \Rightarrow c\right) \Rightarrow \left(\left(a \vee b\right) \Rightarrow c\right) = b \vee c \vee \neg a$$
$$\left(a \Rightarrow b\right) \Rightarrow \left(\left(b \Rightarrow c\right) \Rightarrow \left(\left(a \vee b\right) \Rightarrow c\right)\right) = 1$$
$$b \Rightarrow c = c \vee \neg b$$
$$\left(a \vee b\right) \Rightarrow c = c \vee \left(\neg a \wedge \neg b\right)$$
$$\left(b \Rightarrow c\right) \Rightarrow \left(\left(a \vee b\right) \Rightarrow c\right) = b \vee c \vee \neg a$$
$$\left(a \Rightarrow b\right) \Rightarrow \left(\left(b \Rightarrow c\right) \Rightarrow \left(\left(a \vee b\right) \Rightarrow c\right)\right) = 1$$
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 | +---+---+---+--------+