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