In the sentence "Many lost dogs ______ been given back to their owners", which auxiliary verb correctly completes the present perfect passive?

Introduction / Context:
This grammar question checks your understanding of subject verb agreement and tense formation in the present perfect passive. The sentence talks about lost dogs that have already been returned to their owners. You must choose the auxiliary verb that agrees in number with the subject and completes the present perfect passive structure correctly.

Given Data / Assumptions:

• The sentence is: Many lost dogs ______ been given back to their owners.
• The subject is Many lost dogs, which is clearly plural.
• We want a present perfect passive construction: have/has been + past participle.
• Options: have, is, has, would.

Concept / Approach:
In present perfect passive, the auxiliary have or has is used according to whether the subject is plural or singular. Plural subjects take have and singular third person subjects take has. The passive form of the verb give is been given. Therefore, the correct combination for a plural subject is have been given. Is would form present simple passive, and would would shift the sentence into a different, hypothetical mood.

Step-by-Step Solution:
Step 1: Identify the subject: Many lost dogs. This is clearly plural.Step 2: Recognise that the rest of the verb phrase is been given back, which indicates a passive construction.Step 3: For present perfect passive with a plural subject, use have been given.Step 4: Test have: Many lost dogs have been given back to their owners. This is grammatically correct.Step 5: Test has, is, and would; each one leads to disagreement or incorrect tense and must be rejected.

Verification / Alternative check:
Replace Many lost dogs with a singular subject to compare forms. With a singular subject we would say The lost dog has been given back to its owner. With a plural subject this becomes The lost dogs have been given back to their owners. Our sentence structure matches the plural pattern. Using is would create Many lost dogs is been given back, which is ungrammatical. Using has gives Many lost dogs has been given back, which breaks subject verb agreement. Would been given is also incorrect because would must be followed by be, not been, in such a construction.

Why Other Options Are Wrong:
Is is the third person singular form of the verb be in the present simple and does not match plural subject many lost dogs. Has is the third person singular form of have and cannot agree with a plural subject. Would is a modal that would require a different structure, such as would be given, and would change the meaning from a completed action to a possibility or hypothetical case.

Common Pitfalls:
Students sometimes focus so much on the nearest noun dogs that they forget to check the entire verb phrase, or they may be confused between passive and active forms. A good strategy is always to identify the subject first (singular or plural) and then match the auxiliary have/has accordingly before worrying about the rest of the sentence.

Final Answer:
The correct auxiliary verb is have, giving the sentence Many lost dogs have been given back to their owners, so option A is correct.