Sr Examen
Expresión ((¬b→a∨c))∨((¬a∨b)→c)
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
((¬b)⇒(a∨c))∨((b∨(¬a))⇒c)
$$\left(\neg b \Rightarrow \left(a \vee c\right)\right) \vee \left(\left(b \vee \neg a\right) \Rightarrow c\right)$$
Solución detallada
$$\neg b \Rightarrow \left(a \vee c\right) = a \vee b \vee c$$
$$\left(b \vee \neg a\right) \Rightarrow c = c \vee \left(a \wedge \neg b\right)$$
$$\left(\neg b \Rightarrow \left(a \vee c\right)\right) \vee \left(\left(b \vee \neg a\right) \Rightarrow c\right) = a \vee b \vee c$$
$$\left(b \vee \neg a\right) \Rightarrow c = c \vee \left(a \wedge \neg b\right)$$
$$\left(\neg b \Rightarrow \left(a \vee c\right)\right) \vee \left(\left(b \vee \neg a\right) \Rightarrow c\right) = a \vee b \vee c$$
Tabla de verdad
+---+---+---+--------+ | a | b | c | result | +===+===+===+========+ | 0 | 0 | 0 | 0 | +---+---+---+--------+ | 0 | 0 | 1 | 1 | +---+---+---+--------+ | 0 | 1 | 0 | 1 | +---+---+---+--------+ | 0 | 1 | 1 | 1 | +---+---+---+--------+ | 1 | 0 | 0 | 1 | +---+---+---+--------+ | 1 | 0 | 1 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+