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