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