How are the prophecies proclaimed by the three apparitions in Act IV, Scene 1 fulfilled in Act V of "Macbeth"?

The First Apparition warns Macbeth against Macduff--'Beware of Macduff'. Macbeth is already apprehensive of the Thane of Fife and contemplates his killing. The prophetic warning thus confirms Macbeth's apprehension. Later, in Act V, Macduff beheads Macbeth and the warning comes true.

The Second Apparition, a bloody child, assures Macbeth that no man born of a woman can ever cause any harm to Macbeth. Unable to see through the equivocation, Macbeth feels relieved that Macduff can do him no harm. But later in the Fifth Act, Macduff reveals to Macbeth's disillusion that he was born untimely, and not strictly born of the mother's womb. Macbeth realises how the seemingly assuring prophecy was couched in deceptive language.

The Third Apparition, a crowned child with a tree in its hand, further assures Macbeth that he can never be vanquished until the Birnam Woods comes to the Dunsinane hill. Once again, Macbeth in his credulous over-confidence fails to see the equivocation and feels safe. In the Fifth Act, Malcolm instructs his ten thousand-strong army that each soldier should take a leafy branch from the Birnam Woods to use the same as a cover while marching towards the Dunsinane castle as a tactic of camouflage to shadow their numbers. A servant, confused and alarmed, reports to Macbeth that he has seen a 'moving grove'.