Sr Examen
Expresión ¬(¬(a⇒b)∨((¬c)⇒a))
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
¬(((¬c)⇒a)∨(¬(a⇒b)))
$$\neg \left(\left(\neg c \Rightarrow a\right) \vee a \not\Rightarrow b\right)$$
Solución detallada
$$\neg c \Rightarrow a = a \vee c$$
$$a \Rightarrow b = b \vee \neg a$$
$$a \not\Rightarrow b = a \wedge \neg b$$
$$\left(\neg c \Rightarrow a\right) \vee a \not\Rightarrow b = a \vee c$$
$$\neg \left(\left(\neg c \Rightarrow a\right) \vee a \not\Rightarrow b\right) = \neg a \wedge \neg c$$
$$a \Rightarrow b = b \vee \neg a$$
$$a \not\Rightarrow b = a \wedge \neg b$$
$$\left(\neg c \Rightarrow a\right) \vee a \not\Rightarrow b = a \vee c$$
$$\neg \left(\left(\neg c \Rightarrow a\right) \vee a \not\Rightarrow b\right) = \neg a \wedge \neg c$$
Tabla de verdad
+---+---+---+--------+ | a | b | c | result | +===+===+===+========+ | 0 | 0 | 0 | 1 | +---+---+---+--------+ | 0 | 0 | 1 | 0 | +---+---+---+--------+ | 0 | 1 | 0 | 1 | +---+---+---+--------+ | 0 | 1 | 1 | 0 | +---+---+---+--------+ | 1 | 0 | 0 | 0 | +---+---+---+--------+ | 1 | 0 | 1 | 0 | +---+---+---+--------+ | 1 | 1 | 0 | 0 | +---+---+---+--------+ | 1 | 1 | 1 | 0 | +---+---+---+--------+