Sr Examen
Expresión abV~b~cdV~a~cdV~abcV~a~bcdVab~cd
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Solución
Ha introducido
[src]
(c∧d)⇔((¬a)∨(c∧d))⇔((¬b)∨(a∧b))⇔((a∧b)∨(b∧c∧d))⇔((¬a)∨(c∧d)∨(b∧c∧(¬a)))
$$\left(c \wedge d\right) ⇔ \left(\left(a \wedge b\right) \vee \left(b \wedge c \wedge d\right)\right) ⇔ \left(\left(c \wedge d\right) \vee \neg a\right) ⇔ \left(\left(a \wedge b\right) \vee \neg b\right) ⇔ \left(\left(c \wedge d\right) \vee \left(b \wedge c \wedge \neg a\right) \vee \neg a\right)$$
Solución detallada
$$\left(a \wedge b\right) \vee \neg b = a \vee \neg b$$
$$\left(a \wedge b\right) \vee \left(b \wedge c \wedge d\right) = b \wedge \left(a \vee c\right) \wedge \left(a \vee d\right)$$
$$\left(c \wedge d\right) \vee \left(b \wedge c \wedge \neg a\right) \vee \neg a = \left(c \wedge d\right) \vee \neg a$$
$$\left(c \wedge d\right) ⇔ \left(\left(a \wedge b\right) \vee \left(b \wedge c \wedge d\right)\right) ⇔ \left(\left(c \wedge d\right) \vee \neg a\right) ⇔ \left(\left(a \wedge b\right) \vee \neg b\right) ⇔ \left(\left(c \wedge d\right) \vee \left(b \wedge c \wedge \neg a\right) \vee \neg a\right) = a \wedge b \wedge c \wedge d$$
$$\left(a \wedge b\right) \vee \left(b \wedge c \wedge d\right) = b \wedge \left(a \vee c\right) \wedge \left(a \vee d\right)$$
$$\left(c \wedge d\right) \vee \left(b \wedge c \wedge \neg a\right) \vee \neg a = \left(c \wedge d\right) \vee \neg a$$
$$\left(c \wedge d\right) ⇔ \left(\left(a \wedge b\right) \vee \left(b \wedge c \wedge d\right)\right) ⇔ \left(\left(c \wedge d\right) \vee \neg a\right) ⇔ \left(\left(a \wedge b\right) \vee \neg b\right) ⇔ \left(\left(c \wedge d\right) \vee \left(b \wedge c \wedge \neg a\right) \vee \neg a\right) = a \wedge b \wedge c \wedge d$$
Tabla de verdad
+---+---+---+---+--------+ | a | b | c | d | result | +===+===+===+===+========+ | 0 | 0 | 0 | 0 | 0 | +---+---+---+---+--------+ | 0 | 0 | 0 | 1 | 0 | +---+---+---+---+--------+ | 0 | 0 | 1 | 0 | 0 | +---+---+---+---+--------+ | 0 | 0 | 1 | 1 | 0 | +---+---+---+---+--------+ | 0 | 1 | 0 | 0 | 0 | +---+---+---+---+--------+ | 0 | 1 | 0 | 1 | 0 | +---+---+---+---+--------+ | 0 | 1 | 1 | 0 | 0 | +---+---+---+---+--------+ | 0 | 1 | 1 | 1 | 0 | +---+---+---+---+--------+ | 1 | 0 | 0 | 0 | 0 | +---+---+---+---+--------+ | 1 | 0 | 0 | 1 | 0 | +---+---+---+---+--------+ | 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 | 1 | +---+---+---+---+--------+