Question

1. Swim once a month.
2. Have a swim once a month.
3. Take a swim once a month.
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Are they all grammatical? Do we have to put 'have' or 'take' before 'a swim'?

4. Exercise regularly.
5. Have exercise once a month.
6. Take exercise once a month.
(What about these sentences?)

Answer 1

1, 2, and 3 are all okay. Yes, you need to have a verb to make a sentence. "A swim" is a noun, so you need "Have" or "Take", verbs. You could say "Swim..." (swim is a verb without the "a") "once a month". In that case, the subject, "you", is implied.

In #4, exercise is a verb, so, with the implied subject "you", it's a sentence. In 5 and 6, just as in 2 and 3 above, "exercise" becomes a noun, as "swim" does in 2 and 3, so both are grammatical with the verbs "have" and "take".