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Expresión (a⇒b)∧(b⇒a)⇒a∨b
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Solución
Ha introducido
[src]
((a⇒b)∧(b⇒a))⇒(a∨b)
$$\left(\left(a \Rightarrow b\right) \wedge \left(b \Rightarrow a\right)\right) \Rightarrow \left(a \vee b\right)$$
Solución detallada
$$a \Rightarrow b = b \vee \neg a$$
$$b \Rightarrow a = a \vee \neg b$$
$$\left(a \Rightarrow b\right) \wedge \left(b \Rightarrow a\right) = \left(a \wedge b\right) \vee \left(\neg a \wedge \neg b\right)$$
$$\left(\left(a \Rightarrow b\right) \wedge \left(b \Rightarrow a\right)\right) \Rightarrow \left(a \vee b\right) = a \vee b$$
$$b \Rightarrow a = a \vee \neg b$$
$$\left(a \Rightarrow b\right) \wedge \left(b \Rightarrow a\right) = \left(a \wedge b\right) \vee \left(\neg a \wedge \neg b\right)$$
$$\left(\left(a \Rightarrow b\right) \wedge \left(b \Rightarrow a\right)\right) \Rightarrow \left(a \vee b\right) = a \vee b$$
Tabla de verdad
+---+---+--------+ | a | b | result | +===+===+========+ | 0 | 0 | 0 | +---+---+--------+ | 0 | 1 | 1 | +---+---+--------+ | 1 | 0 | 1 | +---+---+--------+ | 1 | 1 | 1 | +---+---+--------+