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Lógica matemática/ nota(notb+notc)+a×b

Expresión nota(notb+notc)+a×b

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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