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