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