What are the requirements for using a comma or a semicolon to connect two independent clauses?

For a comma you need a FANBOY (for,and, nor, but, or, yet, so) followed by a comma and then your next independent clause.

Example: It was raining on Saturday, so we played board games inside.

For the semicolon, just separate the two clauses with the semicolon.

Example: It was raining on Saturday; we played board games inside.

An independent clause is a group of words that contains a subject and a predicate. It express a complete thought and it can be alone as a sentence. It can also be linked to other dependent or independent clauses to build a more interesting and complex sentence.

Rules for commas: Commas help improve clarity, avoid ambiguity, and indicate where you should pause. Use a comma to join two or more independent clauses. In most cases, place a comma between two sentences that join with a coordinating conjunction (and, but, or, for, nor, so, yet).

Example: The rain stopped, and the sun came out again.

It is not necessary to place a comma between two independent clauses if they are short and have a similar meaning, provided there are no misunderstandings.

Example: Some doctors advertise their services but many doctors find this deplorable.

To avoid confusion, use a comma after an introductory subordinate clause or phrase.

Example: Because of taxes, we need to raise prices in our store.

When a coordinating conjunction "and" is used to connect the last element of a series of three or more elements or clauses, a comma is optional before the conjunction "and". If it is used it is called Oxford comma.

Example: I bought coffee, sugar, biscuits, and milk at the store.

If you only have one clause (a pair of subject and verb), you will not usually need a comma before the conjunction.

Example: I have already sanded the floor of the room but still need to paint the wall.

(This sentence has two verbs but only one subject, so it has only one clause)

Rules for semicolon: Use the semicolon if you have two independent clauses that you are connecting without a coordinating conjunction.  

Example: I've studied a lot; Now I need to be lucky.

Also, use the semicolon when you already have commas for smaller separations, then you will need the semicolon to show a larger separation.

Example: We had a family party with my parents, my brother, my uncle; and my English cousins.

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