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