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