This question tests your understanding of verb patterns and infinitives in English grammar. The sentence structure requires an infinitive (to + base verb) to express purpose or necessity.

The correct answer is "to look after" because:

Step 1: Identify the main verb - "have not got" (meaning "do not have")

Step 2: Recognize that we need to complete the meaning of what you don't have - a child [purpose/function]

Step 3: The infinitive "to look after" correctly shows the purpose or intended function of the child

Step 4: Compare with incorrect options:

• "looking after" - creates a participle phrase that doesn't fit the structure
• "is looking after" - creates a grammatical error (verb conflict)
• "having looked after" - creates an awkward perfect participle that doesn't express purpose

Final Answer: You are lucky you have not got a child to look after.

Related Topics

Infinitives: The base form of a verb preceded by "to" used to express purpose, intention, or necessity.

Verb Patterns: Different structures that follow certain verbs (want to, need to, have to) that require specific forms.

Key Formula/Pattern

Subject + have/has + (not) + object + to + base verb → Expressing what someone has/dosen't have to do

Example: "I have homework to complete" or "She doesn't have anyone to help her"