punctuation - Do I need to use a comma if a subject follows "and" in a sentence?

Mike went to the shop, and he bought vegetables.

or

Mike went to the shop and bought vegetables.

My understanding is that when the subject is there after 'and', the comma is required.

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My understanding is that when there is no subject after 'and', the comma is not required.

Am I correct on the understanding?

Answer

The general rule we can apply here is that the first sentence calls for a comma because it is a compound sentence consisting of two independent clauses joined by a coordinating conjunction (even though the subjects "Mike" and "he" are complementary, referring to the same person):

1 Mike went to the shop.
2 He bought vegetables.

However, the comma is not always required. In shorter sentences, writers often leave out the comma:

I walked and Mike ran.
I called but no one answered.

The second sentence (Mike went to the shop and bought vegetables.) is a simple sentence (one independent clause) with a compound predicate consisting of two verbs ("went" and "bought"), and we should not include a comma.

Note that if the predicate contains three or more verbs, we can apply the "list rule" for commas and separate them:

Mike went to the store, bought groceries, and returned home.