Sr Examen
Lógica matemática/
а3∧а2∧¬а1∧¬а0∨а3∧¬а2∧¬а1∧а0∨¬а3∧¬а2∧а1∧а0∨а3∧а2∧а1∧а0∨¬а3∧а2∧а1∧¬а0а3∧а2∧¬а1∧¬а0∨а3∧¬а2∧¬а1∧а0∨¬а3∧¬а2∧а1∧а0∨а3∧а2∧а1∧а0∨¬а3∧а2∧а1∧¬а0а3∧а2∧¬а1∧¬а0∨а3∧¬а2∧¬а1∧а0∨¬а3∧¬а2∧а1∧а0∨а3∧а2∧а1∧а0∨¬а3∧а2∧а1∧¬а0
Expresión а3∧а2∧¬а1∧¬а0∨а3∧¬а2∧¬а1∧а0∨¬а3∧¬а2∧а1∧а0∨а3∧а2∧а1∧а0∨¬а3∧а2∧а1∧¬а0а3∧а2∧¬а1∧¬а0∨а3∧¬а2∧¬а1∧а0∨¬а3∧¬а2∧а1∧а0∨а3∧а2∧а1∧а0∨¬а3∧а2∧а1∧¬а0а3∧а2∧¬а1∧¬а0∨а3∧¬а2∧¬а1∧а0∨¬а3∧¬а2∧а1∧а0∨а3∧а2∧а1∧а0∨¬а3∧а2∧а1∧¬а0
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
(a0∧a1∧a2∧a3)∨(a0∧a1∧(¬a2)∧(¬a3))∨(a0∧a3∧(¬a1)∧(¬a2))∨(a1∧a2∧(¬a0)∧(¬a3))∨(a2∧a3∧(¬a0)∧(¬a1))∨(a1∧a2∧a3∧(¬a0)∧(¬a1)∧(¬a3))
$$\left(a_{0} \wedge a_{1} \wedge a_{2} \wedge a_{3}\right) \vee \left(a_{0} \wedge a_{1} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{3} \wedge \neg a_{1} \wedge \neg a_{2}\right) \vee \left(a_{1} \wedge a_{2} \wedge \neg a_{0} \wedge \neg a_{3}\right) \vee \left(a_{2} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{1}\right) \vee \left(a_{1} \wedge a_{2} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{1} \wedge \neg a_{3}\right)$$
Solución detallada
$$a_{1} \wedge a_{2} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{1} \wedge \neg a_{3} = \text{False}$$
$$\left(a_{0} \wedge a_{1} \wedge a_{2} \wedge a_{3}\right) \vee \left(a_{0} \wedge a_{1} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{3} \wedge \neg a_{1} \wedge \neg a_{2}\right) \vee \left(a_{1} \wedge a_{2} \wedge \neg a_{0} \wedge \neg a_{3}\right) \vee \left(a_{2} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{1}\right) \vee \left(a_{1} \wedge a_{2} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{1} \wedge \neg a_{3}\right) = \left(a_{0} \vee a_{2}\right) \wedge \left(a_{1} \vee a_{3}\right) \wedge \left(a_{0} \vee \neg a_{1} \vee \neg a_{3}\right) \wedge \left(a_{1} \vee \neg a_{0} \vee \neg a_{2}\right) \wedge \left(a_{2} \vee \neg a_{1} \vee \neg a_{3}\right) \wedge \left(a_{3} \vee \neg a_{0} \vee \neg a_{2}\right)$$
$$\left(a_{0} \wedge a_{1} \wedge a_{2} \wedge a_{3}\right) \vee \left(a_{0} \wedge a_{1} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{3} \wedge \neg a_{1} \wedge \neg a_{2}\right) \vee \left(a_{1} \wedge a_{2} \wedge \neg a_{0} \wedge \neg a_{3}\right) \vee \left(a_{2} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{1}\right) \vee \left(a_{1} \wedge a_{2} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{1} \wedge \neg a_{3}\right) = \left(a_{0} \vee a_{2}\right) \wedge \left(a_{1} \vee a_{3}\right) \wedge \left(a_{0} \vee \neg a_{1} \vee \neg a_{3}\right) \wedge \left(a_{1} \vee \neg a_{0} \vee \neg a_{2}\right) \wedge \left(a_{2} \vee \neg a_{1} \vee \neg a_{3}\right) \wedge \left(a_{3} \vee \neg a_{0} \vee \neg a_{2}\right)$$
Simplificación
[src]
$$\left(a_{0} \vee a_{2}\right) \wedge \left(a_{1} \vee a_{3}\right) \wedge \left(a_{0} \vee \neg a_{1} \vee \neg a_{3}\right) \wedge \left(a_{1} \vee \neg a_{0} \vee \neg a_{2}\right) \wedge \left(a_{2} \vee \neg a_{1} \vee \neg a_{3}\right) \wedge \left(a_{3} \vee \neg a_{0} \vee \neg a_{2}\right)$$
(a0∨a2)∧(a1∨a3)∧(a0∨(¬a1)∨(¬a3))∧(a1∨(¬a0)∨(¬a2))∧(a2∨(¬a1)∨(¬a3))∧(a3∨(¬a0)∨(¬a2))
Tabla de verdad
+----+----+----+----+--------+ | a0 | a1 | a2 | a3 | result | +====+====+====+====+========+ | 0 | 0 | 0 | 0 | 0 | +----+----+----+----+--------+ | 0 | 0 | 0 | 1 | 0 | +----+----+----+----+--------+ | 0 | 0 | 1 | 0 | 0 | +----+----+----+----+--------+ | 0 | 0 | 1 | 1 | 1 | +----+----+----+----+--------+ | 0 | 1 | 0 | 0 | 0 | +----+----+----+----+--------+ | 0 | 1 | 0 | 1 | 0 | +----+----+----+----+--------+ | 0 | 1 | 1 | 0 | 1 | +----+----+----+----+--------+ | 0 | 1 | 1 | 1 | 0 | +----+----+----+----+--------+ | 1 | 0 | 0 | 0 | 0 | +----+----+----+----+--------+ | 1 | 0 | 0 | 1 | 1 | +----+----+----+----+--------+ | 1 | 0 | 1 | 0 | 0 | +----+----+----+----+--------+ | 1 | 0 | 1 | 1 | 0 | +----+----+----+----+--------+ | 1 | 1 | 0 | 0 | 1 | +----+----+----+----+--------+ | 1 | 1 | 0 | 1 | 0 | +----+----+----+----+--------+ | 1 | 1 | 1 | 0 | 0 | +----+----+----+----+--------+ | 1 | 1 | 1 | 1 | 1 | +----+----+----+----+--------+
FNC
[src]
Ya está reducido a FNC
$$\left(a_{0} \vee a_{2}\right) \wedge \left(a_{1} \vee a_{3}\right) \wedge \left(a_{0} \vee \neg a_{1} \vee \neg a_{3}\right) \wedge \left(a_{1} \vee \neg a_{0} \vee \neg a_{2}\right) \wedge \left(a_{2} \vee \neg a_{1} \vee \neg a_{3}\right) \wedge \left(a_{3} \vee \neg a_{0} \vee \neg a_{2}\right)$$
(a0∨a2)∧(a1∨a3)∧(a0∨(¬a1)∨(¬a3))∧(a1∨(¬a0)∨(¬a2))∧(a2∨(¬a1)∨(¬a3))∧(a3∨(¬a0)∨(¬a2))
FNDP
[src]
$$\left(a_{0} \wedge a_{1} \wedge a_{2} \wedge a_{3}\right) \vee \left(a_{0} \wedge a_{1} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{3} \wedge \neg a_{1} \wedge \neg a_{2}\right) \vee \left(a_{1} \wedge a_{2} \wedge \neg a_{0} \wedge \neg a_{3}\right) \vee \left(a_{2} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{1}\right)$$
(a0∧a1∧a2∧a3)∨(a0∧a1∧(¬a2)∧(¬a3))∨(a0∧a3∧(¬a1)∧(¬a2))∨(a1∧a2∧(¬a0)∧(¬a3))∨(a2∧a3∧(¬a0)∧(¬a1))
FNCD
[src]
$$\left(a_{0} \vee a_{2}\right) \wedge \left(a_{1} \vee a_{3}\right) \wedge \left(a_{0} \vee \neg a_{1} \vee \neg a_{3}\right) \wedge \left(a_{1} \vee \neg a_{0} \vee \neg a_{2}\right) \wedge \left(a_{2} \vee \neg a_{1} \vee \neg a_{3}\right) \wedge \left(a_{3} \vee \neg a_{0} \vee \neg a_{2}\right)$$
(a0∨a2)∧(a1∨a3)∧(a0∨(¬a1)∨(¬a3))∧(a1∨(¬a0)∨(¬a2))∧(a2∨(¬a1)∨(¬a3))∧(a3∨(¬a0)∨(¬a2))
FND
[src]
$$\left(a_{0} \wedge a_{1} \wedge a_{2} \wedge a_{3}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{2} \wedge \neg a_{0}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{2} \wedge \neg a_{2}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{3} \wedge \neg a_{1}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{3} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{1} \wedge \neg a_{0} \wedge \neg a_{1}\right) \vee \left(a_{0} \wedge a_{1} \wedge \neg a_{0} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{1} \wedge \neg a_{1} \wedge \neg a_{2}\right) \vee \left(a_{0} \wedge a_{1} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{2} \wedge a_{3} \wedge \neg a_{0}\right) \vee \left(a_{0} \wedge a_{2} \wedge a_{3} \wedge \neg a_{2}\right) \vee \left(a_{0} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{1}\right) \vee \left(a_{0} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{3} \wedge \neg a_{1} \wedge \neg a_{2}\right) \vee \left(a_{0} \wedge a_{3} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{1} \wedge a_{2} \wedge a_{3} \wedge \neg a_{1}\right) \vee \left(a_{1} \wedge a_{2} \wedge a_{3} \wedge \neg a_{3}\right) \vee \left(a_{1} \wedge a_{2} \wedge \neg a_{0} \wedge \neg a_{1}\right) \vee \left(a_{1} \wedge a_{2} \wedge \neg a_{0} \wedge \neg a_{3}\right) \vee \left(a_{1} \wedge a_{2} \wedge \neg a_{1} \wedge \neg a_{2}\right) \vee \left(a_{1} \wedge a_{2} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{2} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{1}\right) \vee \left(a_{2} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{3}\right) \vee \left(a_{2} \wedge a_{3} \wedge \neg a_{1} \wedge \neg a_{2}\right) \vee \left(a_{2} \wedge a_{3} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{2} \wedge a_{3} \wedge \neg a_{0}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{2} \wedge a_{3} \wedge \neg a_{1}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{2} \wedge a_{3} \wedge \neg a_{2}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{2} \wedge a_{3} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{2} \wedge \neg a_{0} \wedge \neg a_{1}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{2} \wedge \neg a_{0} \wedge \neg a_{2}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{2} \wedge \neg a_{0} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{2} \wedge \neg a_{1} \wedge \neg a_{2}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{2} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{1}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{3} \wedge \neg a_{1} \wedge \neg a_{2}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{3} \wedge \neg a_{1} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{3} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{1} \wedge \neg a_{0} \wedge \neg a_{1} \wedge \neg a_{2}\right) \vee \left(a_{0} \wedge a_{1} \wedge \neg a_{0} \wedge \neg a_{1} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{1} \wedge \neg a_{0} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{1} \wedge \neg a_{1} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{2} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{1}\right) \vee \left(a_{0} \wedge a_{2} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{2}\right) \vee \left(a_{0} \wedge a_{2} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{2} \wedge a_{3} \wedge \neg a_{1} \wedge \neg a_{2}\right) \vee \left(a_{0} \wedge a_{2} \wedge a_{3} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{1} \wedge \neg a_{2}\right) \vee \left(a_{0} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{1} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{3} \wedge \neg a_{1} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{1} \wedge a_{2} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{1}\right) \vee \left(a_{1} \wedge a_{2} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{3}\right) \vee \left(a_{1} \wedge a_{2} \wedge a_{3} \wedge \neg a_{1} \wedge \neg a_{2}\right) \vee \left(a_{1} \wedge a_{2} \wedge a_{3} \wedge \neg a_{1} \wedge \neg a_{3}\right) \vee \left(a_{1} \wedge a_{2} \wedge a_{3} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{1} \wedge a_{2} \wedge \neg a_{0} \wedge \neg a_{1} \wedge \neg a_{2}\right) \vee \left(a_{1} \wedge a_{2} \wedge \neg a_{0} \wedge \neg a_{1} \wedge \neg a_{3}\right) \vee \left(a_{1} \wedge a_{2} \wedge \neg a_{0} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{1} \wedge a_{2} \wedge \neg a_{1} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{2} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{1} \wedge \neg a_{2}\right) \vee \left(a_{2} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{1} \wedge \neg a_{3}\right) \vee \left(a_{2} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{2} \wedge a_{3} \wedge \neg a_{1} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{2} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{1}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{2} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{2} \wedge a_{3} \wedge \neg a_{1} \wedge \neg a_{2}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{2} \wedge a_{3} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{2} \wedge \neg a_{0} \wedge \neg a_{1} \wedge \neg a_{2}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{2} \wedge \neg a_{0} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{1} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{1} \wedge a_{3} \wedge \neg a_{1} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{1} \wedge \neg a_{0} \wedge \neg a_{1} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{2} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{1} \wedge \neg a_{2}\right) \vee \left(a_{0} \wedge a_{2} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{0} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{1} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{1} \wedge a_{2} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{1} \wedge \neg a_{3}\right) \vee \left(a_{1} \wedge a_{2} \wedge a_{3} \wedge \neg a_{1} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{1} \wedge a_{2} \wedge \neg a_{0} \wedge \neg a_{1} \wedge \neg a_{2} \wedge \neg a_{3}\right) \vee \left(a_{2} \wedge a_{3} \wedge \neg a_{0} \wedge \neg a_{1} \wedge \neg a_{2} \wedge \neg a_{3}\right)$$
(a0∧a1∧a2∧a3)∨(a0∧a1∧a2∧(¬a0))∨(a0∧a1∧a2∧(¬a2))∨(a0∧a1∧a3∧(¬a1))∨(a0∧a1∧a3∧(¬a3))∨(a0∧a2∧a3∧(¬a0))∨(a0∧a2∧a3∧(¬a2))∨(a1∧a2∧a3∧(¬a1))∨(a1∧a2∧a3∧(¬a3))∨(a0∧a1∧(¬a0)∧(¬a1))∨(a0∧a1∧(¬a0)∧(¬a3))∨(a0∧a1∧(¬a1)∧(¬a2))∨(a0∧a1∧(¬a2)∧(¬a3))∨(a0∧a3∧(¬a0)∧(¬a1))∨(a0∧a3∧(¬a0)∧(¬a3))∨(a0∧a3∧(¬a1)∧(¬a2))∨(a0∧a3∧(¬a2)∧(¬a3))∨(a1∧a2∧(¬a0)∧(¬a1))∨(a1∧a2∧(¬a0)∧(¬a3))∨(a1∧a2∧(¬a1)∧(¬a2))∨(a1∧a2∧(¬a2)∧(¬a3))∨(a2∧a3∧(¬a0)∧(¬a1))∨(a2∧a3∧(¬a0)∧(¬a3))∨(a2∧a3∧(¬a1)∧(¬a2))∨(a2∧a3∧(¬a2)∧(¬a3))∨(a0∧a1∧a2∧a3∧(¬a0))∨(a0∧a1∧a2∧a3∧(¬a1))∨(a0∧a1∧a2∧a3∧(¬a2))∨(a0∧a1∧a2∧a3∧(¬a3))∨(a0∧a1∧a2∧(¬a0)∧(¬a1))∨(a0∧a1∧a2∧(¬a0)∧(¬a2))∨(a0∧a1∧a2∧(¬a0)∧(¬a3))∨(a0∧a1∧a2∧(¬a1)∧(¬a2))∨(a0∧a1∧a2∧(¬a2)∧(¬a3))∨(a0∧a1∧a3∧(¬a0)∧(¬a1))∨(a0∧a1∧a3∧(¬a0)∧(¬a3))∨(a0∧a1∧a3∧(¬a1)∧(¬a2))∨(a0∧a1∧a3∧(¬a1)∧(¬a3))∨(a0∧a1∧a3∧(¬a2)∧(¬a3))∨(a0∧a2∧a3∧(¬a0)∧(¬a1))∨(a0∧a2∧a3∧(¬a0)∧(¬a2))∨(a0∧a2∧a3∧(¬a0)∧(¬a3))∨(a0∧a2∧a3∧(¬a1)∧(¬a2))∨(a0∧a2∧a3∧(¬a2)∧(¬a3))∨(a1∧a2∧a3∧(¬a0)∧(¬a1))∨(a1∧a2∧a3∧(¬a0)∧(¬a3))∨(a1∧a2∧a3∧(¬a1)∧(¬a2))∨(a1∧a2∧a3∧(¬a1)∧(¬a3))∨(a1∧a2∧a3∧(¬a2)∧(¬a3))∨(a0∧a1∧(¬a0)∧(¬a1)∧(¬a2))∨(a0∧a1∧(¬a0)∧(¬a1)∧(¬a3))∨(a0∧a1∧(¬a0)∧(¬a2)∧(¬a3))∨(a0∧a1∧(¬a1)∧(¬a2)∧(¬a3))∨(a0∧a3∧(¬a0)∧(¬a1)∧(¬a2))∨(a0∧a3∧(¬a0)∧(¬a1)∧(¬a3))∨(a0∧a3∧(¬a0)∧(¬a2)∧(¬a3))∨(a0∧a3∧(¬a1)∧(¬a2)∧(¬a3))∨(a1∧a2∧(¬a0)∧(¬a1)∧(¬a2))∨(a1∧a2∧(¬a0)∧(¬a1)∧(¬a3))∨(a1∧a2∧(¬a0)∧(¬a2)∧(¬a3))∨(a1∧a2∧(¬a1)∧(¬a2)∧(¬a3))∨(a2∧a3∧(¬a0)∧(¬a1)∧(¬a2))∨(a2∧a3∧(¬a0)∧(¬a1)∧(¬a3))∨(a2∧a3∧(¬a0)∧(¬a2)∧(¬a3))∨(a2∧a3∧(¬a1)∧(¬a2)∧(¬a3))∨(a0∧a1∧a2∧a3∧(¬a0)∧(¬a1))∨(a0∧a1∧a2∧a3∧(¬a0)∧(¬a3))∨(a0∧a1∧a2∧a3∧(¬a1)∧(¬a2))∨(a0∧a1∧a2∧a3∧(¬a2)∧(¬a3))∨(a0∧a1∧a2∧(¬a0)∧(¬a1)∧(¬a2))∨(a0∧a1∧a2∧(¬a0)∧(¬a2)∧(¬a3))∨(a0∧a1∧a3∧(¬a0)∧(¬a1)∧(¬a3))∨(a0∧a1∧a3∧(¬a1)∧(¬a2)∧(¬a3))∨(a0∧a2∧a3∧(¬a0)∧(¬a1)∧(¬a2))∨(a0∧a2∧a3∧(¬a0)∧(¬a2)∧(¬a3))∨(a1∧a2∧a3∧(¬a0)∧(¬a1)∧(¬a3))∨(a1∧a2∧a3∧(¬a1)∧(¬a2)∧(¬a3))∨(a0∧a1∧(¬a0)∧(¬a1)∧(¬a2)∧(¬a3))∨(a0∧a3∧(¬a0)∧(¬a1)∧(¬a2)∧(¬a3))∨(a1∧a2∧(¬a0)∧(¬a1)∧(¬a2)∧(¬a3))∨(a2∧a3∧(¬a0)∧(¬a1)∧(¬a2)∧(¬a3))