Sr Examen
Expresión xy+((x→z)≡(y→w))
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
(x∧y)∨((x⇒z)⇔(y⇒w))
$$\left(x \wedge y\right) \vee \left(\left(x \Rightarrow z\right) ⇔ \left(y \Rightarrow w\right)\right)$$
Solución detallada
$$x \Rightarrow z = z \vee \neg x$$
$$y \Rightarrow w = w \vee \neg y$$
$$\left(x \Rightarrow z\right) ⇔ \left(y \Rightarrow w\right) = \left(w \wedge z\right) \vee \left(w \wedge \neg x\right) \vee \left(z \wedge \neg y\right) \vee \left(\neg x \wedge \neg y\right) \vee \left(x \wedge y \wedge \neg w \wedge \neg z\right)$$
$$\left(x \wedge y\right) \vee \left(\left(x \Rightarrow z\right) ⇔ \left(y \Rightarrow w\right)\right) = \left(w \wedge \neg x\right) \vee \left(x \wedge y\right) \vee \left(z \wedge \neg y\right) \vee \left(\neg x \wedge \neg y\right)$$
$$y \Rightarrow w = w \vee \neg y$$
$$\left(x \Rightarrow z\right) ⇔ \left(y \Rightarrow w\right) = \left(w \wedge z\right) \vee \left(w \wedge \neg x\right) \vee \left(z \wedge \neg y\right) \vee \left(\neg x \wedge \neg y\right) \vee \left(x \wedge y \wedge \neg w \wedge \neg z\right)$$
$$\left(x \wedge y\right) \vee \left(\left(x \Rightarrow z\right) ⇔ \left(y \Rightarrow w\right)\right) = \left(w \wedge \neg x\right) \vee \left(x \wedge y\right) \vee \left(z \wedge \neg y\right) \vee \left(\neg x \wedge \neg y\right)$$
Simplificación
[src]
$$\left(w \wedge \neg x\right) \vee \left(x \wedge y\right) \vee \left(z \wedge \neg y\right) \vee \left(\neg x \wedge \neg y\right)$$
(x∧y)∨(w∧(¬x))∨(z∧(¬y))∨((¬x)∧(¬y))
Tabla de verdad
+---+---+---+---+--------+ | w | x | y | z | result | +===+===+===+===+========+ | 0 | 0 | 0 | 0 | 1 | +---+---+---+---+--------+ | 0 | 0 | 0 | 1 | 1 | +---+---+---+---+--------+ | 0 | 0 | 1 | 0 | 0 | +---+---+---+---+--------+ | 0 | 0 | 1 | 1 | 0 | +---+---+---+---+--------+ | 0 | 1 | 0 | 0 | 0 | +---+---+---+---+--------+ | 0 | 1 | 0 | 1 | 1 | +---+---+---+---+--------+ | 0 | 1 | 1 | 0 | 1 | +---+---+---+---+--------+ | 0 | 1 | 1 | 1 | 1 | +---+---+---+---+--------+ | 1 | 0 | 0 | 0 | 1 | +---+---+---+---+--------+ | 1 | 0 | 0 | 1 | 1 | +---+---+---+---+--------+ | 1 | 0 | 1 | 0 | 1 | +---+---+---+---+--------+ | 1 | 0 | 1 | 1 | 1 | +---+---+---+---+--------+ | 1 | 1 | 0 | 0 | 0 | +---+---+---+---+--------+ | 1 | 1 | 0 | 1 | 1 | +---+---+---+---+--------+ | 1 | 1 | 1 | 0 | 1 | +---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 1 | +---+---+---+---+--------+
FND
[src]
Ya está reducido a FND
$$\left(w \wedge \neg x\right) \vee \left(x \wedge y\right) \vee \left(z \wedge \neg y\right) \vee \left(\neg x \wedge \neg y\right)$$
(x∧y)∨(w∧(¬x))∨(z∧(¬y))∨((¬x)∧(¬y))
FNC
[src]
$$\left(w \vee x \vee \neg y\right) \wedge \left(w \vee y \vee \neg y\right) \wedge \left(x \vee z \vee \neg x\right) \wedge \left(x \vee \neg x \vee \neg y\right) \wedge \left(y \vee z \vee \neg x\right) \wedge \left(y \vee \neg x \vee \neg y\right) \wedge \left(w \vee x \vee z \vee \neg x\right) \wedge \left(w \vee x \vee z \vee \neg y\right) \wedge \left(w \vee x \vee \neg x \vee \neg y\right) \wedge \left(w \vee y \vee z \vee \neg x\right) \wedge \left(w \vee y \vee z \vee \neg y\right) \wedge \left(w \vee y \vee \neg x \vee \neg y\right) \wedge \left(x \vee z \vee \neg x \vee \neg y\right) \wedge \left(y \vee z \vee \neg x \vee \neg y\right)$$
(w∨x∨(¬y))∧(w∨y∨(¬y))∧(x∨z∨(¬x))∧(y∨z∨(¬x))∧(x∨(¬x)∨(¬y))∧(y∨(¬x)∨(¬y))∧(w∨x∨z∨(¬x))∧(w∨x∨z∨(¬y))∧(w∨y∨z∨(¬x))∧(w∨y∨z∨(¬y))∧(w∨x∨(¬x)∨(¬y))∧(w∨y∨(¬x)∨(¬y))∧(x∨z∨(¬x)∨(¬y))∧(y∨z∨(¬x)∨(¬y))
FNDP
[src]
$$\left(w \wedge \neg x\right) \vee \left(x \wedge y\right) \vee \left(z \wedge \neg y\right) \vee \left(\neg x \wedge \neg y\right)$$
(x∧y)∨(w∧(¬x))∨(z∧(¬y))∨((¬x)∧(¬y))
FNCD
[src]
$$\left(w \vee x \vee \neg y\right) \wedge \left(y \vee z \vee \neg x\right)$$
(w∨x∨(¬y))∧(y∨z∨(¬x))