Please give three examples of truth versus falsehood in Othello.
There are examples everywhere in the play - almost too many to list. Here are three, all from the first scene, Act One, Scene One:
First, one from the end of the scene. Here's Iago talking about Othello to Roderigo:
Though I do hate him as I do hell-pains.
Yet, for necessity of present life,
I must show out a flag and sign of love,
Which is indeed but sign.
Pure and simple, Iago is telling Roderigo that to protect his own life ('for necessity of present life') he is going to have to pretend to show love to Othello - wave a 'flag' (a 'sign') of love - but that 'sign' will be only a sign ('but sign'). It'll look like love, but it'll only look like it - it's an appearance not a reality. A falsehood disguised like a truth.
And, secondly, as I jump to the start of the scene, here's the first two lines of the play for some more:
Tush! never tell me; I take it much unkindly
That thou, Iago, who hast had my purse
As if the strings were thine, shouldst know of this.
'Sblood, but you will not hear me:
If ever I did dream of such a matter,
Roderigo is angry that Iago has known about Othello's marriage; Iago tells him that he never even dreamt of such a thing. Now, Shakespeare doesn't tell us how Iago found out about the marriage, nor do we know if he knew about it beforehand. We don't know whether he's lying or not. Though he lies to Roderigo later, and we know that he has indeed had Roderigo's 'purse / as if the strings were' his own, we don't know whether Iago is genuinely surprised or not.
Point being, the audience don't know whether Iago is telling the truth or not. Nobody knows. What's the truth of the matter here? Did Iago know about the marriage? Who told him? Did he keep it from Roderigo? Shakespeare deliberately leaves it ambiguous.
And this is the problem with truth and falsehood in this play. We never find out for absolute certain whether Desdemona and Cassio have slept together (it would be SO easy for Shakespeare to write a short scene for the two characters together to confirm that it never happened. But he doesn't). We never find out for certain whether Othello and Emilia have had an affair (Iago certainly thinks so). You don't know whether anyone is really what they claim to be or not.
And Iago even admits this:
I am not what I am.
True line or false line? Well, it's both. He's admitting to lying ('I'm not what I seem to be'). But he's being honest about lying. He's being truthful about his blatant falseness. And just like everything else in the play, you're not quite sure what to do with him - not quite sure what to believe. He's the liar who everyone thinks is 'honest' (go through and count the number of times they call him that!).
So truth and falsehood in this play are difficult categories to separate. But it's a great question!