Expresión (x⇔¬yz)⇒(x⇔¬yt)

Ha introducido [src]

(x⇔(z∧(¬y)))⇒(x⇔(t∧(¬y)))

\left(x ⇔ \left(z \wedge \neg y\right)\right) \Rightarrow \left(x ⇔ \left(t \wedge \neg y\right)\right)

Solución detallada

x ⇔ \left(z \wedge \neg y\right) = \left(y \wedge \neg x\right) \vee \left(\neg x \wedge \neg z\right) \vee \left(x \wedge z \wedge \neg y\right)

x ⇔ \left(t \wedge \neg y\right) = \left(y \wedge \neg x\right) \vee \left(\neg t \wedge \neg x\right) \vee \left(t \wedge x \wedge \neg y\right)

\left(x ⇔ \left(z \wedge \neg y\right)\right) \Rightarrow \left(x ⇔ \left(t \wedge \neg y\right)\right) = y \vee \left(t \wedge x\right) \vee \left(t \wedge z\right) \vee \left(x \wedge \neg z\right) \vee \left(z \wedge \neg x\right) \vee \left(\neg t \wedge \neg x\right) \vee \left(\neg t \wedge \neg z\right)

Simplificación [src]

y \vee \left(t \wedge x\right) \vee \left(t \wedge z\right) \vee \left(x \wedge \neg z\right) \vee \left(z \wedge \neg x\right) \vee \left(\neg t \wedge \neg x\right) \vee \left(\neg t \wedge \neg z\right)

y∨(t∧x)∨(t∧z)∨(x∧(¬z))∨(z∧(¬x))∨((¬t)∧(¬x))∨((¬t)∧(¬z))

Tabla de verdad

+---+---+---+---+--------+
| t | x | y | z | result |
+===+===+===+===+========+
| 0 | 0 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 1      |
+---+---+---+---+--------+

FNC [src]

\left(t \vee y \vee \neg x \vee \neg z\right) \wedge \left(x \vee y \vee z \vee \neg t\right) \wedge \left(t \vee x \vee y \vee z \vee \neg t\right) \wedge \left(t \vee x \vee y \vee \neg t \vee \neg x\right) \wedge \left(t \vee x \vee y \vee \neg x \vee \neg z\right) \wedge \left(t \vee y \vee z \vee \neg t \vee \neg z\right) \wedge \left(t \vee y \vee z \vee \neg x \vee \neg z\right) \wedge \left(t \vee y \vee \neg t \vee \neg x \vee \neg z\right) \wedge \left(x \vee y \vee z \vee \neg t \vee \neg x\right) \wedge \left(x \vee y \vee z \vee \neg t \vee \neg z\right) \wedge \left(x \vee y \vee z \vee \neg x \vee \neg z\right) \wedge \left(t \vee x \vee y \vee z \vee \neg t \vee \neg x\right) \wedge \left(t \vee x \vee y \vee z \vee \neg t \vee \neg z\right) \wedge \left(t \vee x \vee y \vee z \vee \neg x \vee \neg z\right) \wedge \left(t \vee x \vee y \vee \neg t \vee \neg x \vee \neg z\right) \wedge \left(t \vee y \vee z \vee \neg t \vee \neg x \vee \neg z\right) \wedge \left(x \vee y \vee z \vee \neg t \vee \neg x \vee \neg z\right) \wedge \left(t \vee x \vee y \vee z \vee \neg t \vee \neg x \vee \neg z\right)

(x∨y∨z∨(¬t))∧(t∨y∨(¬x)∨(¬z))∧(t∨x∨y∨z∨(¬t))∧(t∨x∨y∨(¬t)∨(¬x))∧(t∨x∨y∨(¬x)∨(¬z))∧(t∨y∨z∨(¬t)∨(¬z))∧(t∨y∨z∨(¬x)∨(¬z))∧(x∨y∨z∨(¬t)∨(¬x))∧(x∨y∨z∨(¬t)∨(¬z))∧(x∨y∨z∨(¬x)∨(¬z))∧(t∨y∨(¬t)∨(¬x)∨(¬z))∧(t∨x∨y∨z∨(¬t)∨(¬x))∧(t∨x∨y∨z∨(¬t)∨(¬z))∧(t∨x∨y∨z∨(¬x)∨(¬z))∧(t∨x∨y∨(¬t)∨(¬x)∨(¬z))∧(t∨y∨z∨(¬t)∨(¬x)∨(¬z))∧(x∨y∨z∨(¬t)∨(¬x)∨(¬z))∧(t∨x∨y∨z∨(¬t)∨(¬x)∨(¬z))

FNCD [src]

\left(t \vee y \vee \neg x \vee \neg z\right) \wedge \left(x \vee y \vee z \vee \neg t\right)

(x∨y∨z∨(¬t))∧(t∨y∨(¬x)∨(¬z))

FND [src]

Ya está reducido a FND

y \vee \left(t \wedge x\right) \vee \left(t \wedge z\right) \vee \left(x \wedge \neg z\right) \vee \left(z \wedge \neg x\right) \vee \left(\neg t \wedge \neg x\right) \vee \left(\neg t \wedge \neg z\right)

y∨(t∧x)∨(t∧z)∨(x∧(¬z))∨(z∧(¬x))∨((¬t)∧(¬x))∨((¬t)∧(¬z))

FNDP [src]

y \vee \left(t \wedge x\right) \vee \left(t \wedge z\right) \vee \left(x \wedge \neg z\right) \vee \left(z \wedge \neg x\right) \vee \left(\neg t \wedge \neg x\right) \vee \left(\neg t \wedge \neg z\right)

y∨(t∧x)∨(t∧z)∨(x∧(¬z))∨(z∧(¬x))∨((¬t)∧(¬x))∨((¬t)∧(¬z))

¿Cómo usar?

Expresiones idénticas

Expresión (x⇔¬yz)⇒(x⇔¬yt)

Solución