Sr Examen
Expresión A∧B→(A∨B)∧C∨C~(¬A∨B)∧¬C
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
((¬c)∧(b∨(¬a)))⇔((a∧b)⇒(c∨(c∧(a∨b))))
$$\left(\neg c \wedge \left(b \vee \neg a\right)\right) ⇔ \left(\left(a \wedge b\right) \Rightarrow \left(c \vee \left(c \wedge \left(a \vee b\right)\right)\right)\right)$$
Solución detallada
$$c \vee \left(c \wedge \left(a \vee b\right)\right) = c$$
$$\left(a \wedge b\right) \Rightarrow \left(c \vee \left(c \wedge \left(a \vee b\right)\right)\right) = c \vee \neg a \vee \neg b$$
$$\left(\neg c \wedge \left(b \vee \neg a\right)\right) ⇔ \left(\left(a \wedge b\right) \Rightarrow \left(c \vee \left(c \wedge \left(a \vee b\right)\right)\right)\right) = \neg a \wedge \neg c$$
$$\left(a \wedge b\right) \Rightarrow \left(c \vee \left(c \wedge \left(a \vee b\right)\right)\right) = c \vee \neg a \vee \neg b$$
$$\left(\neg c \wedge \left(b \vee \neg a\right)\right) ⇔ \left(\left(a \wedge b\right) \Rightarrow \left(c \vee \left(c \wedge \left(a \vee b\right)\right)\right)\right) = \neg a \wedge \neg c$$
Tabla de verdad
+---+---+---+--------+ | a | b | c | result | +===+===+===+========+ | 0 | 0 | 0 | 1 | +---+---+---+--------+ | 0 | 0 | 1 | 0 | +---+---+---+--------+ | 0 | 1 | 0 | 1 | +---+---+---+--------+ | 0 | 1 | 1 | 0 | +---+---+---+--------+ | 1 | 0 | 0 | 0 | +---+---+---+--------+ | 1 | 0 | 1 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 0 | +---+---+---+--------+