Sr Examen
Expresión ∼{∼(p⇔q)∧∼(q∧q)}
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Solución
Solución detallada
$$p ⇔ q = \left(p \wedge q\right) \vee \left(\neg p \wedge \neg q\right)$$
$$p \not\equiv q = \left(p \wedge \neg q\right) \vee \left(q \wedge \neg p\right)$$
$$\neg q \wedge p \not\equiv q = p \wedge \neg q$$
$$\neg \left(\neg q \wedge p \not\equiv q\right) = q \vee \neg p$$
$$p \not\equiv q = \left(p \wedge \neg q\right) \vee \left(q \wedge \neg p\right)$$
$$\neg q \wedge p \not\equiv q = p \wedge \neg q$$
$$\neg \left(\neg q \wedge p \not\equiv q\right) = q \vee \neg p$$
Tabla de verdad
+---+---+--------+ | p | q | result | +===+===+========+ | 0 | 0 | 1 | +---+---+--------+ | 0 | 1 | 1 | +---+---+--------+ | 1 | 0 | 0 | +---+---+--------+ | 1 | 1 | 1 | +---+---+--------+