Step 1: Understanding the Concept:
This question tests the use of infinitives and gerunds as predicate nominatives (a noun or pronoun that renames the subject). The sentence structure is "Subject + Verb 'to be' + Complement".
Step 2: Detailed Explanation:
1. Analyze the Sentence Structure: The subject is "Their idea of a holiday". The verb is "is". The sentence needs a complement to explain what the idea is. Both an infinitive ("to" + base verb) and a gerund (verb + "-ing") can function as a noun here.
2. Evaluate the Options:
- (A) is relaxed: "Relaxed" is a past participle acting as an adjective. It would mean the idea itself is in a state of relaxation, which is illogical.
- (B) is to relaxing: This is a grammatically incorrect structure. The preposition "to" cannot be followed by a gerund ("relaxing") in this context.
- (C) is to relax: This uses the infinitive form "to relax". This structure is commonly used to state a purpose, goal, or idea. "Their idea is to relax" correctly and clearly states the content of their idea.
- (D) is relaxing: This uses the gerund "relaxing". While "Their idea is relaxing" is grammatically possible, it could be ambiguous. It might mean that the idea itself is relaxing (adjective), or it could mean the idea consists of the act of relaxing (gerund). Option (C) is more precise and common for expressing a plan or idea.
Step 3: Final Answer:
The clearest and most standard grammatical choice to express the content of an "idea" is the infinitive form. Therefore, (C) "is to relax" is the best answer.