1. I would rather die than surrender.
2. I would rather fail than cheat.
3. I would rather play games than study.
4. I would rather walk to work than go to work by car.
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Are they all grammatical? Do we have to use the base verb after 'than'? Can we use a 'to-infinitive' after 'than'? What is the part of speech of 'than' in each sentence? What could be the full form of 'the expression' after 'than'?
These are all fine, yes.
You can either use the base verb or the infinitive, although the infinitive form is a bit wordy. Most people don't use it in this expression.
1. "I would rather die than surrender." - This sentence is grammatically correct. The word "than" is used as a conjunction to introduce the second part of the comparison. In this case, the base verb "surrender" is used correctly after "than."
2. "I would rather fail than cheat." - This sentence is also grammatically correct. Again, "than" is used as a conjunction, and the base verb "cheat" is used after it.
3. "I would rather play games than study." - This sentence is also grammatically correct. "Than" is still used as a conjunction, and the base verb "study" is used after it.
4. "I would rather walk to work than go to work by car." - This sentence is grammatically correct. In this case, "than" is used as a conjunction, and the base verb "go" is used after it.
In all these sentences, the word "than" is a conjunction used to introduce the second part of a comparison. It is not a preposition, so it does not take a "to-infinitive" after it.
The full form of the expression after "than" is typically a finite clause (a group of words that includes a subject and a verb). For example, in the first sentence, "surrender" is a verb in the base form, but it is part of the finite clause "I would rather die." Similarly, in the fourth sentence, "go" is the base verb, but it is part of the finite clause "I would rather go to work by car."
Overall, in these examples, both the base verb and the finite clause are grammatically correct usages.