Fill in the blank in the following sentence with the most appropriate…

The correct answer is Option (3) → nor

"Nor" after a negative clause:

• Nor means "and not"; it adds a second negative idea to a first negative one.
• After nor the helping verb comes before the subject (inversion): nor do I wish, nor did she write.
• Deciding clue: the negative "have not met" and the inverted "do I wish" after the blank.
• This sentence: "I have not met him" is negative, and the second part adds another negative idea with inversion, "nor do I wish to meet him".
• Complete sentence: I have not met him, nor do I wish to meet him.
  Example: She did not call, nor did she write.

Why the Other Options are Incorrect?

Option 1: or — Incorrect. Or offers a choice; it does not carry the negative forward and is not followed by inversion.
Example: Would you like tea or coffee?

Option 2: so — Incorrect. So shows a result; not wishing to meet him is not a result of not having met him.
Example: It was late, so we left.

Option 4: yet — Incorrect. Yet shows contrast; the two parts agree, they do not contrast.
Example: He is rich, yet he is unhappy.

Contrast: "nor" adds a second negative idea, with inversion; "or" offers a choice, "so" shows a result and "yet" shows contrast.