Sr Examen
Expresión (x⇒(y⇒z))⇒(x^y⇒z)
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
(x⇒(y⇒z))⇒((x∧y)⇒z)
$$\left(x \Rightarrow \left(y \Rightarrow z\right)\right) \Rightarrow \left(\left(x \wedge y\right) \Rightarrow z\right)$$
Solución detallada
$$y \Rightarrow z = z \vee \neg y$$
$$x \Rightarrow \left(y \Rightarrow z\right) = z \vee \neg x \vee \neg y$$
$$\left(x \wedge y\right) \Rightarrow z = z \vee \neg x \vee \neg y$$
$$\left(x \Rightarrow \left(y \Rightarrow z\right)\right) \Rightarrow \left(\left(x \wedge y\right) \Rightarrow z\right) = 1$$
$$x \Rightarrow \left(y \Rightarrow z\right) = z \vee \neg x \vee \neg y$$
$$\left(x \wedge y\right) \Rightarrow z = z \vee \neg x \vee \neg y$$
$$\left(x \Rightarrow \left(y \Rightarrow z\right)\right) \Rightarrow \left(\left(x \wedge y\right) \Rightarrow z\right) = 1$$
Tabla de verdad
+---+---+---+--------+ | x | y | z | 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 | +---+---+---+--------+