Sr Examen
Expresión not(m1¬(m2)vm3¬(m1))vnot((not(m1¬(m2))vm3))&m1
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
(m1∧(¬(m3∨(¬(m1∧(¬m2))))))∨(¬((m1∧(¬m2))∨(m3∧(¬m1))))
$$\left(m_{1} \wedge \neg \left(m_{3} \vee \neg \left(m_{1} \wedge \neg m_{2}\right)\right)\right) \vee \neg \left(\left(m_{1} \wedge \neg m_{2}\right) \vee \left(m_{3} \wedge \neg m_{1}\right)\right)$$
Solución detallada
$$\neg \left(m_{1} \wedge \neg m_{2}\right) = m_{2} \vee \neg m_{1}$$
$$m_{3} \vee \neg \left(m_{1} \wedge \neg m_{2}\right) = m_{2} \vee m_{3} \vee \neg m_{1}$$
$$\neg \left(m_{3} \vee \neg \left(m_{1} \wedge \neg m_{2}\right)\right) = m_{1} \wedge \neg m_{2} \wedge \neg m_{3}$$
$$m_{1} \wedge \neg \left(m_{3} \vee \neg \left(m_{1} \wedge \neg m_{2}\right)\right) = m_{1} \wedge \neg m_{2} \wedge \neg m_{3}$$
$$\neg \left(\left(m_{1} \wedge \neg m_{2}\right) \vee \left(m_{3} \wedge \neg m_{1}\right)\right) = \left(m_{1} \wedge m_{2}\right) \vee \left(\neg m_{1} \wedge \neg m_{3}\right)$$
$$\left(m_{1} \wedge \neg \left(m_{3} \vee \neg \left(m_{1} \wedge \neg m_{2}\right)\right)\right) \vee \neg \left(\left(m_{1} \wedge \neg m_{2}\right) \vee \left(m_{3} \wedge \neg m_{1}\right)\right) = \left(m_{1} \wedge m_{2}\right) \vee \neg m_{3}$$
$$m_{3} \vee \neg \left(m_{1} \wedge \neg m_{2}\right) = m_{2} \vee m_{3} \vee \neg m_{1}$$
$$\neg \left(m_{3} \vee \neg \left(m_{1} \wedge \neg m_{2}\right)\right) = m_{1} \wedge \neg m_{2} \wedge \neg m_{3}$$
$$m_{1} \wedge \neg \left(m_{3} \vee \neg \left(m_{1} \wedge \neg m_{2}\right)\right) = m_{1} \wedge \neg m_{2} \wedge \neg m_{3}$$
$$\neg \left(\left(m_{1} \wedge \neg m_{2}\right) \vee \left(m_{3} \wedge \neg m_{1}\right)\right) = \left(m_{1} \wedge m_{2}\right) \vee \left(\neg m_{1} \wedge \neg m_{3}\right)$$
$$\left(m_{1} \wedge \neg \left(m_{3} \vee \neg \left(m_{1} \wedge \neg m_{2}\right)\right)\right) \vee \neg \left(\left(m_{1} \wedge \neg m_{2}\right) \vee \left(m_{3} \wedge \neg m_{1}\right)\right) = \left(m_{1} \wedge m_{2}\right) \vee \neg m_{3}$$
Tabla de verdad
+----+----+----+--------+ | m1 | m2 | m3 | result | +====+====+====+========+ | 0 | 0 | 0 | 1 | +----+----+----+--------+ | 0 | 0 | 1 | 0 | +----+----+----+--------+ | 0 | 1 | 0 | 1 | +----+----+----+--------+ | 0 | 1 | 1 | 0 | +----+----+----+--------+ | 1 | 0 | 0 | 1 | +----+----+----+--------+ | 1 | 0 | 1 | 0 | +----+----+----+--------+ | 1 | 1 | 0 | 1 | +----+----+----+--------+ | 1 | 1 | 1 | 1 | +----+----+----+--------+
FNCD
[src]
$$\left(m_{1} \vee \neg m_{3}\right) \wedge \left(m_{2} \vee \neg m_{3}\right)$$
(m1∨(¬m3))∧(m2∨(¬m3))
FNC
[src]
$$\left(m_{1} \vee \neg m_{3}\right) \wedge \left(m_{2} \vee \neg m_{3}\right)$$
(m1∨(¬m3))∧(m2∨(¬m3))