Expresión ((¬a→¬b∧(a→c)))⊕(d≡a)

Ha introducido [src]

(a⇔d)⊕((¬a)⇒((¬b)∧(a⇒c)))

$$\left(a ⇔ d\right) ⊕ \left(\neg a \Rightarrow \left(\left(a \Rightarrow c\right) \wedge \neg b\right)\right)$$

Вы использовали:
⊕ - Сложение по модулю 2 (Исключающее или).
Возможно вы имели ввиду символ ∨ - Дизъюнкция (ИЛИ)?
Посмотреть с символом ∨

Solución detallada

$$a ⇔ d = \left(a \wedge d\right) \vee \left(\neg a \wedge \neg d\right)$$
$$a \Rightarrow c = c \vee \neg a$$
$$\left(a \Rightarrow c\right) \wedge \neg b = \neg b \wedge \left(c \vee \neg a\right)$$
$$\neg a \Rightarrow \left(\left(a \Rightarrow c\right) \wedge \neg b\right) = a \vee \neg b$$
$$\left(a ⇔ d\right) ⊕ \left(\neg a \Rightarrow \left(\left(a \Rightarrow c\right) \wedge \neg b\right)\right) = \left(a \wedge \neg d\right) \vee \left(b \wedge \neg d\right) \vee \left(d \wedge \neg a \wedge \neg b\right)$$

Simplificación [src]

$$\left(a \wedge \neg d\right) \vee \left(b \wedge \neg d\right) \vee \left(d \wedge \neg a \wedge \neg b\right)$$

(a∧(¬d))∨(b∧(¬d))∨(d∧(¬a)∧(¬b))

Tabla de verdad

+---+---+---+---+--------+
| a | b | c | d | result |
+===+===+===+===+========+
| 0 | 0 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 0      |
+---+---+---+---+--------+

FNC [src]

$$\left(d \vee \neg d\right) \wedge \left(\neg a \vee \neg d\right) \wedge \left(\neg b \vee \neg d\right) \wedge \left(a \vee b \vee d\right) \wedge \left(a \vee b \vee \neg a\right) \wedge \left(a \vee b \vee \neg b\right) \wedge \left(a \vee d \vee \neg d\right) \wedge \left(a \vee \neg a \vee \neg d\right) \wedge \left(a \vee \neg b \vee \neg d\right) \wedge \left(b \vee d \vee \neg d\right) \wedge \left(b \vee \neg a \vee \neg d\right) \wedge \left(b \vee \neg b \vee \neg d\right)$$

(d∨(¬d))∧(a∨b∨d)∧((¬a)∨(¬d))∧((¬b)∨(¬d))∧(a∨b∨(¬a))∧(a∨b∨(¬b))∧(a∨d∨(¬d))∧(b∨d∨(¬d))∧(a∨(¬a)∨(¬d))∧(a∨(¬b)∨(¬d))∧(b∨(¬a)∨(¬d))∧(b∨(¬b)∨(¬d))

FNDP [src]

$$\left(a \wedge \neg d\right) \vee \left(b \wedge \neg d\right) \vee \left(d \wedge \neg a \wedge \neg b\right)$$

(a∧(¬d))∨(b∧(¬d))∨(d∧(¬a)∧(¬b))

FNCD [src]

$$\left(\neg a \vee \neg d\right) \wedge \left(\neg b \vee \neg d\right) \wedge \left(a \vee b \vee d\right)$$

(a∨b∨d)∧((¬a)∨(¬d))∧((¬b)∨(¬d))

FND [src]

Ya está reducido a FND

$$\left(a \wedge \neg d\right) \vee \left(b \wedge \neg d\right) \vee \left(d \wedge \neg a \wedge \neg b\right)$$

(a∧(¬d))∨(b∧(¬d))∨(d∧(¬a)∧(¬b))

¿Cómo usar?

Expresiones idénticas

Expresión ((¬a→¬b∧(a→c)))⊕(d≡a)

Solución