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