Final answer:
The question asks about the correct use of gerunds (-ing form) and infinitives ('to' form) with various verbs in English. It involves understanding the nuances of English grammar and the context in which these forms are used.
Step-by-step explanation:
The question deals with the use of gerunds and infinitives in English grammar. Gerunds are verb forms ending in -ing that function as nouns, while infinitives are the 'to' form of the verb. Both can be used after certain verbs with either similar or different meanings, depending on the context. The question provides pairs of verbs such as 'begin/start doing' and 'continue to propose,' asking to identify the correct form.
In examples with verbs of perception like 'see/hear/watch,' you can use either the base form of the verb (without 'to') or a gerund (-ing form). For instance:
- I heard the dog bark/barking.
- She saw the athlete run/running.
These phrases illustrate how you might structure sentences using the verbs in question.