Sr Examen
Expresión ABC∨ĀBC∨ĀBC⇒(A∨B)∧(A∨C)
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Solución
Ha introducido
[src]
((a∧b∧c)∨(b∧c∧(¬a)))⇒((a∨b)∧(a∨c))
$$\left(\left(a \wedge b \wedge c\right) \vee \left(b \wedge c \wedge \neg a\right)\right) \Rightarrow \left(\left(a \vee b\right) \wedge \left(a \vee c\right)\right)$$
Solución detallada
$$\left(a \wedge b \wedge c\right) \vee \left(b \wedge c \wedge \neg a\right) = b \wedge c$$
$$\left(a \vee b\right) \wedge \left(a \vee c\right) = a \vee \left(b \wedge c\right)$$
$$\left(\left(a \wedge b \wedge c\right) \vee \left(b \wedge c \wedge \neg a\right)\right) \Rightarrow \left(\left(a \vee b\right) \wedge \left(a \vee c\right)\right) = 1$$
$$\left(a \vee b\right) \wedge \left(a \vee c\right) = a \vee \left(b \wedge c\right)$$
$$\left(\left(a \wedge b \wedge c\right) \vee \left(b \wedge c \wedge \neg a\right)\right) \Rightarrow \left(\left(a \vee b\right) \wedge \left(a \vee c\right)\right) = 1$$
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 | 1 | +---+---+---+--------+