Sr Examen
Expresión (!a⇒b*c)+(!(b⇒a*c)⊕b)
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Solución
Ha introducido
[src]
((¬a)⇒(b∧c))∨(b⊕(¬(b⇒(a∧c))))
$$\left(\neg a \Rightarrow \left(b \wedge c\right)\right) \vee \left(b ⊕ b \not\Rightarrow \left(a \wedge c\right)\right)$$
Solución detallada
$$\neg a \Rightarrow \left(b \wedge c\right) = a \vee \left(b \wedge c\right)$$
$$b \Rightarrow \left(a \wedge c\right) = \left(a \wedge c\right) \vee \neg b$$
$$b \not\Rightarrow \left(a \wedge c\right) = b \wedge \left(\neg a \vee \neg c\right)$$
$$b ⊕ b \not\Rightarrow \left(a \wedge c\right) = a \wedge b \wedge c$$
$$\left(\neg a \Rightarrow \left(b \wedge c\right)\right) \vee \left(b ⊕ b \not\Rightarrow \left(a \wedge c\right)\right) = a \vee \left(b \wedge c\right)$$
$$b \Rightarrow \left(a \wedge c\right) = \left(a \wedge c\right) \vee \neg b$$
$$b \not\Rightarrow \left(a \wedge c\right) = b \wedge \left(\neg a \vee \neg c\right)$$
$$b ⊕ b \not\Rightarrow \left(a \wedge c\right) = a \wedge b \wedge c$$
$$\left(\neg a \Rightarrow \left(b \wedge c\right)\right) \vee \left(b ⊕ b \not\Rightarrow \left(a \wedge c\right)\right) = a \vee \left(b \wedge c\right)$$
Tabla de verdad
+---+---+---+--------+ | a | b | c | result | +===+===+===+========+ | 0 | 0 | 0 | 0 | +---+---+---+--------+ | 0 | 0 | 1 | 0 | +---+---+---+--------+ | 0 | 1 | 0 | 0 | +---+---+---+--------+ | 0 | 1 | 1 | 1 | +---+---+---+--------+ | 1 | 0 | 0 | 1 | +---+---+---+--------+ | 1 | 0 | 1 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+