Sr Examen
Expresión pv(p∧q)v(p∧q∧r)v(p∧q∧r∧s)v(p∧q∧r∧s∧t)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
p∨(p∧q)∨(p∧q∧r)∨(p∧q∧r∧s)∨(p∧q∧r∧s∧t)
$$p \vee \left(p \wedge q\right) \vee \left(p \wedge q \wedge r\right) \vee \left(p \wedge q \wedge r \wedge s\right) \vee \left(p \wedge q \wedge r \wedge s \wedge t\right)$$
Solución detallada
$$p \vee \left(p \wedge q\right) \vee \left(p \wedge q \wedge r\right) \vee \left(p \wedge q \wedge r \wedge s\right) \vee \left(p \wedge q \wedge r \wedge s \wedge t\right) = p$$
Tabla de verdad
+---+---+---+---+---+--------+ | p | q | r | s | t | result | +===+===+===+===+===+========+ | 0 | 0 | 0 | 0 | 0 | 0 | +---+---+---+---+---+--------+ | 0 | 0 | 0 | 0 | 1 | 0 | +---+---+---+---+---+--------+ | 0 | 0 | 0 | 1 | 0 | 0 | +---+---+---+---+---+--------+ | 0 | 0 | 0 | 1 | 1 | 0 | +---+---+---+---+---+--------+ | 0 | 0 | 1 | 0 | 0 | 0 | +---+---+---+---+---+--------+ | 0 | 0 | 1 | 0 | 1 | 0 | +---+---+---+---+---+--------+ | 0 | 0 | 1 | 1 | 0 | 0 | +---+---+---+---+---+--------+ | 0 | 0 | 1 | 1 | 1 | 0 | +---+---+---+---+---+--------+ | 0 | 1 | 0 | 0 | 0 | 0 | +---+---+---+---+---+--------+ | 0 | 1 | 0 | 0 | 1 | 0 | +---+---+---+---+---+--------+ | 0 | 1 | 0 | 1 | 0 | 0 | +---+---+---+---+---+--------+ | 0 | 1 | 0 | 1 | 1 | 0 | +---+---+---+---+---+--------+ | 0 | 1 | 1 | 0 | 0 | 0 | +---+---+---+---+---+--------+ | 0 | 1 | 1 | 0 | 1 | 0 | +---+---+---+---+---+--------+ | 0 | 1 | 1 | 1 | 0 | 0 | +---+---+---+---+---+--------+ | 0 | 1 | 1 | 1 | 1 | 0 | +---+---+---+---+---+--------+ | 1 | 0 | 0 | 0 | 0 | 1 | +---+---+---+---+---+--------+ | 1 | 0 | 0 | 0 | 1 | 1 | +---+---+---+---+---+--------+ | 1 | 0 | 0 | 1 | 0 | 1 | +---+---+---+---+---+--------+ | 1 | 0 | 0 | 1 | 1 | 1 | +---+---+---+---+---+--------+ | 1 | 0 | 1 | 0 | 0 | 1 | +---+---+---+---+---+--------+ | 1 | 0 | 1 | 0 | 1 | 1 | +---+---+---+---+---+--------+ | 1 | 0 | 1 | 1 | 0 | 1 | +---+---+---+---+---+--------+ | 1 | 0 | 1 | 1 | 1 | 1 | +---+---+---+---+---+--------+ | 1 | 1 | 0 | 0 | 0 | 1 | +---+---+---+---+---+--------+ | 1 | 1 | 0 | 0 | 1 | 1 | +---+---+---+---+---+--------+ | 1 | 1 | 0 | 1 | 0 | 1 | +---+---+---+---+---+--------+ | 1 | 1 | 0 | 1 | 1 | 1 | +---+---+---+---+---+--------+ | 1 | 1 | 1 | 0 | 0 | 1 | +---+---+---+---+---+--------+ | 1 | 1 | 1 | 0 | 1 | 1 | +---+---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 0 | 1 | +---+---+---+---+---+--------+ | 1 | 1 | 1 | 1 | 1 | 1 | +---+---+---+---+---+--------+