Sr Examen
Expresión ¬[(A^B)v(B^C)v(A^C)v(B^D)]^¬(A^B^C^Dv1)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(¬(True))∧(¬((a∧b)∨(a∧c)∨(b∧c)∨(b∧d)))
$$\neg \left(\text{True}\right) \wedge \neg \left(\left(a \wedge b\right) \vee \left(a \wedge c\right) \vee \left(b \wedge c\right) \vee \left(b \wedge d\right)\right)$$
Solución detallada
$$\neg \left(\text{True}\right) = \text{False}$$
$$\neg \left(\left(a \wedge b\right) \vee \left(a \wedge c\right) \vee \left(b \wedge c\right) \vee \left(b \wedge d\right)\right) = \left(\neg a \vee \neg b\right) \wedge \left(\neg a \vee \neg c\right) \wedge \left(\neg b \vee \neg c\right) \wedge \left(\neg b \vee \neg d\right)$$
$$\neg \left(\text{True}\right) \wedge \neg \left(\left(a \wedge b\right) \vee \left(a \wedge c\right) \vee \left(b \wedge c\right) \vee \left(b \wedge d\right)\right) = \text{False}$$
$$\neg \left(\left(a \wedge b\right) \vee \left(a \wedge c\right) \vee \left(b \wedge c\right) \vee \left(b \wedge d\right)\right) = \left(\neg a \vee \neg b\right) \wedge \left(\neg a \vee \neg c\right) \wedge \left(\neg b \vee \neg c\right) \wedge \left(\neg b \vee \neg d\right)$$
$$\neg \left(\text{True}\right) \wedge \neg \left(\left(a \wedge b\right) \vee \left(a \wedge c\right) \vee \left(b \wedge c\right) \vee \left(b \wedge d\right)\right) = \text{False}$$
Tabla de verdad
+---+---+---+---+--------+ | a | b | c | d | result | +===+===+===+===+========+ | 0 | 0 | 0 | 0 | 1 | +---+---+---+---+--------+ | 0 | 0 | 0 | 1 | 1 | +---+---+---+---+--------+ | 0 | 0 | 1 | 0 | 1 | +---+---+---+---+--------+ | 0 | 0 | 1 | 1 | 1 | +---+---+---+---+--------+ | 0 | 1 | 0 | 0 | 1 | +---+---+---+---+--------+ | 0 | 1 | 0 | 1 | 0 | +---+---+---+---+--------+ | 0 | 1 | 1 | 0 | 0 | +---+---+---+---+--------+ | 0 | 1 | 1 | 1 | 0 | +---+---+---+---+--------+ | 1 | 0 | 0 | 0 | 1 | +---+---+---+---+--------+ | 1 | 0 | 0 | 1 | 1 | +---+---+---+---+--------+ | 1 | 0 | 1 | 0 | 0 | +---+---+---+---+--------+ | 1 | 0 | 1 | 1 | 0 | +---+---+---+---+--------+ | 1 | 1 | 0 | 0 | 0 | +---+---+---+---+--------+ | 1 | 1 | 0 | 1 | 0 | +---+---+---+---+--------+ | 1 | 1 | 1 | 0 | 0 | +---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 0 | +---+---+---+---+--------+