Sr Examen
Lógica matemática/ (P→Q)∧(R→S)

Expresión (P→Q)∧(R→S)

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

    Ha introducido [src] 
    (p⇒q)∧(r⇒s)
    $$\left(p \Rightarrow q\right) \wedge \left(r \Rightarrow s\right)$$
    Solución detallada
    $$p \Rightarrow q = q \vee \neg p$$
    $$r \Rightarrow s = s \vee \neg r$$
    $$\left(p \Rightarrow q\right) \wedge \left(r \Rightarrow s\right) = \left(q \wedge s\right) \vee \left(q \wedge \neg r\right) \vee \left(s \wedge \neg p\right) \vee \left(\neg p \wedge \neg r\right)$$
    Simplificación [src]
    $$\left(q \wedge s\right) \vee \left(q \wedge \neg r\right) \vee \left(s \wedge \neg p\right) \vee \left(\neg p \wedge \neg r\right)$$ 
    (q∧s)∨(q∧(¬r))∨(s∧(¬p))∨((¬p)∧(¬r))
    Tabla de verdad 
    +---+---+---+---+--------+
| p | q | r | s | result |
+===+===+===+===+========+
| 0 | 0 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 1      |
+---+---+---+---+--------+
    FNDP [src]
    $$\left(q \wedge s\right) \vee \left(q \wedge \neg r\right) \vee \left(s \wedge \neg p\right) \vee \left(\neg p \wedge \neg r\right)$$ 
    (q∧s)∨(q∧(¬r))∨(s∧(¬p))∨((¬p)∧(¬r))
    FNC [src]
    $$\left(q \vee \neg p\right) \wedge \left(s \vee \neg r\right) \wedge \left(q \vee s \vee \neg p\right) \wedge \left(q \vee s \vee \neg r\right) \wedge \left(q \vee \neg p \vee \neg r\right) \wedge \left(s \vee \neg p \vee \neg r\right) \wedge \left(q \vee s \vee \neg p \vee \neg r\right)$$ 
    (q∨(¬p))∧(s∨(¬r))∧(q∨s∨(¬p))∧(q∨s∨(¬r))∧(q∨(¬p)∨(¬r))∧(s∨(¬p)∨(¬r))∧(q∨s∨(¬p)∨(¬r))
    FNCD [src]
    $$\left(q \vee \neg p\right) \wedge \left(s \vee \neg r\right)$$ 
    (q∨(¬p))∧(s∨(¬r))
    FND [src]
    Ya está reducido a FND
    $$\left(q \wedge s\right) \vee \left(q \wedge \neg r\right) \vee \left(s \wedge \neg p\right) \vee \left(\neg p \wedge \neg r\right)$$ 
    (q∧s)∨(q∧(¬r))∨(s∧(¬p))∨((¬p)∧(¬r))
    © Sr Examen