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Lógica matemática/ (A⇔B)∧(C⇔D)

Expresión (A⇔B)∧(C⇔D)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

    Ha introducido [src] 
    (a⇔b)∧(c⇔d)
    $$\left(a ⇔ b\right) \wedge \left(c ⇔ d\right)$$
    Solución detallada
    $$a ⇔ b = \left(a \wedge b\right) \vee \left(\neg a \wedge \neg b\right)$$
    $$c ⇔ d = \left(c \wedge d\right) \vee \left(\neg c \wedge \neg d\right)$$
    $$\left(a ⇔ b\right) \wedge \left(c ⇔ d\right) = \left(a \vee \neg b\right) \wedge \left(b \vee \neg a\right) \wedge \left(c \vee \neg d\right) \wedge \left(d \vee \neg c\right)$$
    Simplificación [src]
    $$\left(a \vee \neg b\right) \wedge \left(b \vee \neg a\right) \wedge \left(c \vee \neg d\right) \wedge \left(d \vee \neg c\right)$$ 
    (a∨(¬b))∧(b∨(¬a))∧(c∨(¬d))∧(d∨(¬c))
    Tabla de verdad 
    +---+---+---+---+--------+
| a | b | c | d | result |
+===+===+===+===+========+
| 0 | 0 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 1      |
+---+---+---+---+--------+
    FND [src]
    $$\left(a \wedge b \wedge c \wedge d\right) \vee \left(a \wedge b \wedge c \wedge \neg c\right) \vee \left(a \wedge b \wedge d \wedge \neg d\right) \vee \left(a \wedge b \wedge \neg c \wedge \neg d\right) \vee \left(a \wedge c \wedge d \wedge \neg a\right) \vee \left(a \wedge c \wedge \neg a \wedge \neg c\right) \vee \left(a \wedge d \wedge \neg a \wedge \neg d\right) \vee \left(a \wedge \neg a \wedge \neg c \wedge \neg d\right) \vee \left(b \wedge c \wedge d \wedge \neg b\right) \vee \left(b \wedge c \wedge \neg b \wedge \neg c\right) \vee \left(b \wedge d \wedge \neg b \wedge \neg d\right) \vee \left(b \wedge \neg b \wedge \neg c \wedge \neg d\right) \vee \left(c \wedge d \wedge \neg a \wedge \neg b\right) \vee \left(c \wedge \neg a \wedge \neg b \wedge \neg c\right) \vee \left(d \wedge \neg a \wedge \neg b \wedge \neg d\right) \vee \left(\neg a \wedge \neg b \wedge \neg c \wedge \neg d\right)$$ 
    (a∧b∧c∧d)∨(a∧b∧c∧(¬c))∨(a∧b∧d∧(¬d))∨(a∧c∧d∧(¬a))∨(b∧c∧d∧(¬b))∨(a∧b∧(¬c)∧(¬d))∨(a∧c∧(¬a)∧(¬c))∨(a∧d∧(¬a)∧(¬d))∨(b∧c∧(¬b)∧(¬c))∨(b∧d∧(¬b)∧(¬d))∨(c∧d∧(¬a)∧(¬b))∨(a∧(¬a)∧(¬c)∧(¬d))∨(b∧(¬b)∧(¬c)∧(¬d))∨(c∧(¬a)∧(¬b)∧(¬c))∨(d∧(¬a)∧(¬b)∧(¬d))∨((¬a)∧(¬b)∧(¬c)∧(¬d))
    FNDP [src]
    $$\left(a \wedge b \wedge c \wedge d\right) \vee \left(a \wedge b \wedge \neg c \wedge \neg d\right) \vee \left(c \wedge d \wedge \neg a \wedge \neg b\right) \vee \left(\neg a \wedge \neg b \wedge \neg c \wedge \neg d\right)$$ 
    (a∧b∧c∧d)∨(a∧b∧(¬c)∧(¬d))∨(c∧d∧(¬a)∧(¬b))∨((¬a)∧(¬b)∧(¬c)∧(¬d))
    FNCD [src]
    $$\left(a \vee \neg b\right) \wedge \left(b \vee \neg a\right) \wedge \left(c \vee \neg d\right) \wedge \left(d \vee \neg c\right)$$ 
    (a∨(¬b))∧(b∨(¬a))∧(c∨(¬d))∧(d∨(¬c))
    FNC [src]
    Ya está reducido a FNC
    $$\left(a \vee \neg b\right) \wedge \left(b \vee \neg a\right) \wedge \left(c \vee \neg d\right) \wedge \left(d \vee \neg c\right)$$ 
    (a∨(¬b))∧(b∨(¬a))∧(c∨(¬d))∧(d∨(¬c))
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