Sr Examen
Expresión not(p⊕q)⊕notpv(q&r)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(¬(p⊕q))⊕((¬p)∨(q∧r))
$$\neg \left(p ⊕ q\right) ⊕ \left(\left(q \wedge r\right) \vee \neg p\right)$$
Solución detallada
$$p ⊕ q = \left(p \wedge \neg q\right) \vee \left(q \wedge \neg p\right)$$
$$\neg \left(p ⊕ q\right) = \left(p \wedge q\right) \vee \left(\neg p \wedge \neg q\right)$$
$$\neg \left(p ⊕ q\right) ⊕ \left(\left(q \wedge r\right) \vee \neg p\right) = q \wedge \left(\neg p \vee \neg r\right)$$
$$\neg \left(p ⊕ q\right) = \left(p \wedge q\right) \vee \left(\neg p \wedge \neg q\right)$$
$$\neg \left(p ⊕ q\right) ⊕ \left(\left(q \wedge r\right) \vee \neg p\right) = q \wedge \left(\neg p \vee \neg r\right)$$
Tabla de verdad
+---+---+---+--------+ | p | q | r | 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 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 0 | +---+---+---+--------+