The following sentence has a blank that must be filled with an appropriate word or expression so that the sentence sounds natural and grammatically correct. They have not had much time for social activities and I have not __________ .

Introduction:
This fill in the blank question checks your understanding of how English speakers express similarity in negative sentences. The sentence compares the lack of time for social activities between "they" and "I". You must choose the word or phrase that correctly completes the pattern "They have not ..., and I have not ... either".

Given Data / Assumptions:
- The incomplete sentence reads: "They have not had much time for social activities and I have not __________ ."
- Options are: "done so", "either", "also", and "gone".
- We assume normal conversational and written English usage regarding negative agreement (showing that the same negative statement is true for another person).

Concept / Approach:
In English, when you want to say that a negative statement applies to another person as well, you often use "either" at the end of the second clause. For example, "She does not like coffee, and he does not either." While "also" is used in positive statements, "either" is preferred in negative ones. The phrase "done so" is sometimes used to avoid repetition, but it does not fit neatly here without additional context. The word "gone" does not relate meaningfully to the idea of social activities in this structure.

Step-by-Step Solution:
Step 1: Look at the first half of the sentence: "They have not had much time for social activities."Step 2: Notice that the second half is negative as well: "I have not ..." and must express the same lack of time.Step 3: Test "either": "They have not had much time for social activities and I have not either." This is a standard, natural pattern in English.Step 4: Test "also": "They have not had much time for social activities and I have not also." This sounds unnatural because "also" is usually used with positive statements or with different word order.Step 5: Test "done so" and "gone". "Done so" would normally require a specific action, such as "done so for years," while "gone" does not complete the meaning properly. Thus, "either" is the best choice.

Verification / Alternative check:
Compare similar sentences: "He has not finished his homework, and I have not either," or "They do not watch television, and we do not either." In each case, "either" is the correct word to echo the negative idea. If you try to use "also" in these sentences, they sound wrong or awkward. This confirms that "either" is the expected answer in the exam context.

Why Other Options Are Wrong:
Option A, "done so", could be used in a different structure such as "They have not done so, and I have not done so either," but here the verb "had" and the phrase "much time for social activities" make this replacement odd and incomplete. Option C, "also", is used with positive verbs, for example, "I have also gone," and is incorrect in this negative structure. Option D, "gone", has no clear object or link to "social activities" in this context and does not complete the idea. Only option B, "either", correctly expresses negative agreement.

Common Pitfalls:
Students often confuse "also" and "either", especially when translating directly from their mother tongue. It is important to remember that "also" usually goes with positive statements and "either" with negative statements at the end of a clause. Another pitfall is overusing longer phrases like "done so" even when a single word such as "either" is more appropriate and idiomatic. Practising common patterns like "I do not like it either" will help fix this usage in your memory.

Final Answer:
The sentence is correctly completed as "They have not had much time for social activities and I have not either."