Sr Examen
Expresión a∧b∨c∧a→a∧b
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Solución
Ha introducido
[src]
((a∧b)∨(a∧c))⇒(a∧b)
$$\left(\left(a \wedge b\right) \vee \left(a \wedge c\right)\right) \Rightarrow \left(a \wedge b\right)$$
Solución detallada
$$\left(a \wedge b\right) \vee \left(a \wedge c\right) = a \wedge \left(b \vee c\right)$$
$$\left(\left(a \wedge b\right) \vee \left(a \wedge c\right)\right) \Rightarrow \left(a \wedge b\right) = b \vee \neg a \vee \neg c$$
$$\left(\left(a \wedge b\right) \vee \left(a \wedge c\right)\right) \Rightarrow \left(a \wedge b\right) = b \vee \neg a \vee \neg c$$
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 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+