Sr Examen
Expresión ￢((￢P∧Q)∨￢(R∨￢S))
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
¬((q∧(¬p))∨(¬(r∨(¬s))))
$$\neg \left(\left(q \wedge \neg p\right) \vee \neg \left(r \vee \neg s\right)\right)$$
Solución detallada
$$\neg \left(r \vee \neg s\right) = s \wedge \neg r$$
$$\left(q \wedge \neg p\right) \vee \neg \left(r \vee \neg s\right) = \left(q \vee s\right) \wedge \left(q \vee \neg r\right) \wedge \left(s \vee \neg p\right) \wedge \left(\neg p \vee \neg r\right)$$
$$\neg \left(\left(q \wedge \neg p\right) \vee \neg \left(r \vee \neg s\right)\right) = \left(p \wedge r\right) \vee \left(p \wedge \neg s\right) \vee \left(r \wedge \neg q\right) \vee \left(\neg q \wedge \neg s\right)$$
$$\left(q \wedge \neg p\right) \vee \neg \left(r \vee \neg s\right) = \left(q \vee s\right) \wedge \left(q \vee \neg r\right) \wedge \left(s \vee \neg p\right) \wedge \left(\neg p \vee \neg r\right)$$
$$\neg \left(\left(q \wedge \neg p\right) \vee \neg \left(r \vee \neg s\right)\right) = \left(p \wedge r\right) \vee \left(p \wedge \neg s\right) \vee \left(r \wedge \neg q\right) \vee \left(\neg q \wedge \neg s\right)$$
Simplificación
[src]
$$\left(p \wedge r\right) \vee \left(p \wedge \neg s\right) \vee \left(r \wedge \neg q\right) \vee \left(\neg q \wedge \neg s\right)$$
(p∧r)∨(p∧(¬s))∨(r∧(¬q))∨((¬q)∧(¬s))
Tabla de verdad
+---+---+---+---+--------+ | p | q | r | s | result | +===+===+===+===+========+ | 0 | 0 | 0 | 0 | 1 | +---+---+---+---+--------+ | 0 | 0 | 0 | 1 | 0 | +---+---+---+---+--------+ | 0 | 0 | 1 | 0 | 1 | +---+---+---+---+--------+ | 0 | 0 | 1 | 1 | 1 | +---+---+---+---+--------+ | 0 | 1 | 0 | 0 | 0 | +---+---+---+---+--------+ | 0 | 1 | 0 | 1 | 0 | +---+---+---+---+--------+ | 0 | 1 | 1 | 0 | 0 | +---+---+---+---+--------+ | 0 | 1 | 1 | 1 | 0 | +---+---+---+---+--------+ | 1 | 0 | 0 | 0 | 1 | +---+---+---+---+--------+ | 1 | 0 | 0 | 1 | 0 | +---+---+---+---+--------+ | 1 | 0 | 1 | 0 | 1 | +---+---+---+---+--------+ | 1 | 0 | 1 | 1 | 1 | +---+---+---+---+--------+ | 1 | 1 | 0 | 0 | 1 | +---+---+---+---+--------+ | 1 | 1 | 0 | 1 | 0 | +---+---+---+---+--------+ | 1 | 1 | 1 | 0 | 1 | +---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 1 | +---+---+---+---+--------+
FNDP
[src]
$$\left(p \wedge r\right) \vee \left(p \wedge \neg s\right) \vee \left(r \wedge \neg q\right) \vee \left(\neg q \wedge \neg s\right)$$
(p∧r)∨(p∧(¬s))∨(r∧(¬q))∨((¬q)∧(¬s))
FND
[src]
Ya está reducido a FND
$$\left(p \wedge r\right) \vee \left(p \wedge \neg s\right) \vee \left(r \wedge \neg q\right) \vee \left(\neg q \wedge \neg s\right)$$
(p∧r)∨(p∧(¬s))∨(r∧(¬q))∨((¬q)∧(¬s))
FNC
[src]
$$\left(p \vee \neg q\right) \wedge \left(r \vee \neg s\right) \wedge \left(p \vee r \vee \neg q\right) \wedge \left(p \vee r \vee \neg s\right) \wedge \left(p \vee \neg q \vee \neg s\right) \wedge \left(r \vee \neg q \vee \neg s\right) \wedge \left(p \vee r \vee \neg q \vee \neg s\right)$$
(p∨(¬q))∧(r∨(¬s))∧(p∨r∨(¬q))∧(p∨r∨(¬s))∧(p∨(¬q)∨(¬s))∧(r∨(¬q)∨(¬s))∧(p∨r∨(¬q)∨(¬s))