Sr Examen
Expresión xy+xz+yz=xy+xz
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Solución
Ha introducido
[src]
((x∧y)∨(x∧z))⇔((x∧y)∨(x∧z)∨(y∧z))
$$\left(\left(x \wedge y\right) \vee \left(x \wedge z\right)\right) ⇔ \left(\left(x \wedge y\right) \vee \left(x \wedge z\right) \vee \left(y \wedge z\right)\right)$$
Solución detallada
$$\left(x \wedge y\right) \vee \left(x \wedge z\right) = x \wedge \left(y \vee z\right)$$
$$\left(\left(x \wedge y\right) \vee \left(x \wedge z\right)\right) ⇔ \left(\left(x \wedge y\right) \vee \left(x \wedge z\right) \vee \left(y \wedge z\right)\right) = x \vee \neg y \vee \neg z$$
$$\left(\left(x \wedge y\right) \vee \left(x \wedge z\right)\right) ⇔ \left(\left(x \wedge y\right) \vee \left(x \wedge z\right) \vee \left(y \wedge z\right)\right) = x \vee \neg y \vee \neg z$$
Tabla de verdad
+---+---+---+--------+ | x | y | z | result | +===+===+===+========+ | 0 | 0 | 0 | 1 | +---+---+---+--------+ | 0 | 0 | 1 | 1 | +---+---+---+--------+ | 0 | 1 | 0 | 1 | +---+---+---+--------+ | 0 | 1 | 1 | 0 | +---+---+---+--------+ | 1 | 0 | 0 | 1 | +---+---+---+--------+ | 1 | 0 | 1 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+