Sr Examen
Expresión pv[(qvr)∧(~rvq)]v(~p∧q)v(~q∧~p)
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
p∨(q∧(¬p))∨((¬p)∧(¬q))∨((q∨r)∧(q∨(¬r)))
$$p \vee \left(q \wedge \neg p\right) \vee \left(\neg p \wedge \neg q\right) \vee \left(\left(q \vee r\right) \wedge \left(q \vee \neg r\right)\right)$$
Solución detallada
$$\left(q \vee r\right) \wedge \left(q \vee \neg r\right) = q$$
$$p \vee \left(q \wedge \neg p\right) \vee \left(\neg p \wedge \neg q\right) \vee \left(\left(q \vee r\right) \wedge \left(q \vee \neg r\right)\right) = 1$$
$$p \vee \left(q \wedge \neg p\right) \vee \left(\neg p \wedge \neg q\right) \vee \left(\left(q \vee r\right) \wedge \left(q \vee \neg r\right)\right) = 1$$
Tabla de verdad
+---+---+---+--------+ | p | q | r | result | +===+===+===+========+ | 0 | 0 | 0 | 1 | +---+---+---+--------+ | 0 | 0 | 1 | 1 | +---+---+---+--------+ | 0 | 1 | 0 | 1 | +---+---+---+--------+ | 0 | 1 | 1 | 1 | +---+---+---+--------+ | 1 | 0 | 0 | 1 | +---+---+---+--------+ | 1 | 0 | 1 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+