Sr Examen
Lógica matemática/ notA=>(B+(notB=>(C+notD))=>(A+notF))

Expresión notA=>(B+(notB=>(C+notD))=>(A+notF))

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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