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