Identify the examples of the correct use of Metaphor from the followi…

The correct answer is Option (4) → (A) and (D) only

Metaphor: a metaphor compares two unlike things without "like" or "as", either by saying that one thing is another or by giving it the action of the other.

(A) He is the vulture of the state. — Correct.

• The man is directly called a vulture, without "like" or "as": he preys on the state and lives off its weakness, as a vulture feeds on the dead.

(B) She behaved like a child. — Incorrect.

• The comparison uses "like", so it is a simile, not a metaphor.

(C) To err is human, to forgive divine. — Incorrect.

• This line from Alexander Pope's "An Essay on Criticism" is an epigram: a short, pointed saying that states a general truth.
• Nothing is compared to anything else.

(D) The waves thundered on the shore — Correct.

• The verb "thundered" gives the waves the action of thunder.
• The crash of the waves is compared to thunder without "like" or "as", which makes it an implied metaphor.

Contrast: a simile compares two things openly with "like" or "as". A metaphor makes the comparison without them.