Sr Examen
Lógica matemática/ (dcv!(c->db))bv!(dc<->cvbc)->b

Expresión (dcv!(c->db))bv!(dc<->cvbc)->b

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

    Ha introducido [src] 
    ((¬((c∧d)⇔(c∨(b∧c))))∨(b∧((c∧d)∨(¬(c⇒(b∧d))))))⇒b
    $$\left(\left(b \wedge \left(\left(c \wedge d\right) \vee c \not\Rightarrow \left(b \wedge d\right)\right)\right) \vee \left(c \wedge d\right) \not\equiv \left(c \vee \left(b \wedge c\right)\right)\right) \Rightarrow b$$
    Solución detallada
    $$c \vee \left(b \wedge c\right) = c$$
    $$\left(c \wedge d\right) ⇔ \left(c \vee \left(b \wedge c\right)\right) = d \vee \neg c$$
    $$\left(c \wedge d\right) \not\equiv \left(c \vee \left(b \wedge c\right)\right) = c \wedge \neg d$$
    $$c \Rightarrow \left(b \wedge d\right) = \left(b \wedge d\right) \vee \neg c$$
    $$c \not\Rightarrow \left(b \wedge d\right) = c \wedge \left(\neg b \vee \neg d\right)$$
    $$\left(c \wedge d\right) \vee c \not\Rightarrow \left(b \wedge d\right) = c$$
    $$b \wedge \left(\left(c \wedge d\right) \vee c \not\Rightarrow \left(b \wedge d\right)\right) = b \wedge c$$
    $$\left(b \wedge \left(\left(c \wedge d\right) \vee c \not\Rightarrow \left(b \wedge d\right)\right)\right) \vee \left(c \wedge d\right) \not\equiv \left(c \vee \left(b \wedge c\right)\right) = c \wedge \left(b \vee \neg d\right)$$
    $$\left(\left(b \wedge \left(\left(c \wedge d\right) \vee c \not\Rightarrow \left(b \wedge d\right)\right)\right) \vee \left(c \wedge d\right) \not\equiv \left(c \vee \left(b \wedge c\right)\right)\right) \Rightarrow b = b \vee d \vee \neg c$$
    Simplificación [src]
    $$b \vee d \vee \neg c$$ 
    b∨d∨(¬c)
    Tabla de verdad 
    +---+---+---+--------+
| b | c | d | result |
+===+===+===+========+
| 0 | 0 | 0 | 1      |
+---+---+---+--------+
| 0 | 0 | 1 | 1      |
+---+---+---+--------+
| 0 | 1 | 0 | 0      |
+---+---+---+--------+
| 0 | 1 | 1 | 1      |
+---+---+---+--------+
| 1 | 0 | 0 | 1      |
+---+---+---+--------+
| 1 | 0 | 1 | 1      |
+---+---+---+--------+
| 1 | 1 | 0 | 1      |
+---+---+---+--------+
| 1 | 1 | 1 | 1      |
+---+---+---+--------+
    FND [src]
    Ya está reducido a FND
    $$b \vee d \vee \neg c$$ 
    b∨d∨(¬c)
    FNDP [src]
    $$b \vee d \vee \neg c$$ 
    b∨d∨(¬c)
    FNCD [src]
    $$b \vee d \vee \neg c$$ 
    b∨d∨(¬c)
    FNC [src]
    Ya está reducido a FNC
    $$b \vee d \vee \neg c$$ 
    b∨d∨(¬c)
    © Sr Examen