Sr Examen
Expresión ¬a&bv(¬(b&c))v(¬(a&b⇒c))
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
(b∧(¬a))∨(¬(b∧c))∨(¬((a∧b)⇒c))
$$\left(b \wedge \neg a\right) \vee \neg \left(b \wedge c\right) \vee \left(a \wedge b\right) \not\Rightarrow c$$
Solución detallada
$$\neg \left(b \wedge c\right) = \neg b \vee \neg c$$
$$\left(a \wedge b\right) \Rightarrow c = c \vee \neg a \vee \neg b$$
$$\left(a \wedge b\right) \not\Rightarrow c = a \wedge b \wedge \neg c$$
$$\left(b \wedge \neg a\right) \vee \neg \left(b \wedge c\right) \vee \left(a \wedge b\right) \not\Rightarrow c = \neg a \vee \neg b \vee \neg c$$
$$\left(a \wedge b\right) \Rightarrow c = c \vee \neg a \vee \neg b$$
$$\left(a \wedge b\right) \not\Rightarrow c = a \wedge b \wedge \neg c$$
$$\left(b \wedge \neg a\right) \vee \neg \left(b \wedge c\right) \vee \left(a \wedge b\right) \not\Rightarrow c = \neg a \vee \neg b \vee \neg c$$
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 | 0 | +---+---+---+--------+