In the play Oedipus Rex, Jocasta and Oedipus disagree about what it will take to prove Oedipus' guilt in the murder of King Laius.  On one hand, Oedipus argues that he will receive confirmation of his guilt if the witness (the herdsman/shepherd) confirms that it was a single man that killed the king rather than a mob of robbers.  Conversely, Jocasta argues that it is impossible for Oedipus' guilt to be proved because the oracle predicted that her son would kill Laius, and she knows that her son died in infancy.  She truly believes that her trusted servant murdered the infant Oedipus under her direction.  While Jocasta truly attempts to convince Oedipus to stop his search he is not deterred by her arguments.  

When considering Jocasta's motivation for attempting to convince Oedipus to discontinue his search for the truth, we must understand the fear that Jocasta feels about the possibility of having married her own son.  It is clear that Jocasta feels anxious about the possibility of their marriage being incestuous, and she does not want Oedipus to confirm her fears.  It is due to this fear that Jocasta does everything in her power to dissuade Oedipus from continuing his search.