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