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