In Macbeth, the witches end the first scene with a paradox, "Fair is foul, and foul is fair." Explain fully how this paradox is shown to be true in...

"Fair is foul and foul is fair" means that what seems fair or good is really bad, and what seems bad is really good. Appearances are deceiving. Macbeth seems to be the epitome of the perfect thane (lord), a fearless general who has, without thought for his own safety, charged into battle against the invading Norwegian army. Duncan praises him by saying, essentially, that he can't praise him enough. Macbeth responds with the most modest...

"Fair is foul and foul is fair" means that what seems fair or good is really bad, and what seems bad is really good. Appearances are deceiving. Macbeth seems to be the epitome of the perfect thane (lord), a fearless general who has, without thought for his own safety, charged into battle against the invading Norwegian army. Duncan praises him by saying, essentially, that he can't praise him enough. Macbeth responds with the most modest words imaginable, essentially saying that he has only done his duty to his king. He is, at this point, an honorable man, a great leader. By the end of Act 1, he will be a murderer. 

Lady Macbeth, also, is--as far as we know--a good wife who loves her husband and dotes on him. She is perceived by others to be a gracious hostess, worthy of her station. But even when we meet her, we see the foulness she is planning.

The thane of Cawdor, on the other hand, is a foul man who turns fair in the end. He allied in some way with the Norwegian army. They lost and he was captured. He lost his titles and lands and was sentenced to die. Knowing he had done wrong, Malcolm tells his father: 

But I have spoke
With one that saw him die: who did report
That very frankly he confess'd his treasons,
Implored your highness' pardon and set forth
A deep repentance: nothing in his life
Became him like the leaving it; he died
As one that had been studied in his death
To throw away the dearest thing he owed,
As 'twere a careless trifle.

This is one of the most beautiful eulogies to a death in all of Shakespeare, and it's spoken of the last words and actions of a traitor to the crown.