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