Sr Examen
Expresión ¬(avb⇒a&b)⇔a
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Solución
Ha introducido
[src]
a⇔(¬((a∨b)⇒(a∧b)))
$$a ⇔ \left(a \vee b\right) \not\Rightarrow \left(a \wedge b\right)$$
Solución detallada
$$\left(a \vee b\right) \Rightarrow \left(a \wedge b\right) = \left(a \wedge b\right) \vee \left(\neg a \wedge \neg b\right)$$
$$\left(a \vee b\right) \not\Rightarrow \left(a \wedge b\right) = \left(a \wedge \neg b\right) \vee \left(b \wedge \neg a\right)$$
$$a ⇔ \left(a \vee b\right) \not\Rightarrow \left(a \wedge b\right) = \neg b$$
$$\left(a \vee b\right) \not\Rightarrow \left(a \wedge b\right) = \left(a \wedge \neg b\right) \vee \left(b \wedge \neg a\right)$$
$$a ⇔ \left(a \vee b\right) \not\Rightarrow \left(a \wedge b\right) = \neg b$$
Tabla de verdad
+---+---+--------+ | a | b | result | +===+===+========+ | 0 | 0 | 1 | +---+---+--------+ | 0 | 1 | 0 | +---+---+--------+ | 1 | 0 | 1 | +---+---+--------+ | 1 | 1 | 0 | +---+---+--------+