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