Question regarding combining two independent clauses using colons [duplicate]

After doing research on the proper way of combining two independent clauses using colons, I wanted to confirm that the examples below are using them correctly.

From my research, the second independent clause should interpret or amplify the first.

I'd appreciate any feedback on this topic.

Example 1:

• Ask yourself why you haven't gained muscle: is it because you haven't been to the gym?

Example 2:

• The chair is blue: it was painted by a famous artist who wanted to represent the sky.

Example 3:

• Tell me why you're mad: I'm assuming it's because I didn't call you.

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Also, I've read that capitalizing the letter after the colon is a style choice unless we're discussing proper nouns, lists, or sentence fragments. Is this true?

Solution 1:

Yes, to all your questions.

Here is the relevant discussion from CGEL (p. 1743; note that asyndetic means that the coordination in question does not use an explicit coordinator such as and, but, etc.):

Asyndetic combinations of main clauses

…

■ Colon

[18]  i  Roosevelt was not a socialist: his solution was not to eliminate capital, but to
             tame and regulate it so that it could coexist harmoniously with labour.
        ii  He told us his preference: Jan would take Spanish; Betty would take French.
       iii  The rules were clear: they were not allowed to speak to the committee directly.
       iv  Brown pointed out the costs to the community on the radio last night, and
            McReady mentioned the political consequence in this morning's paper: the bill
             will cost the taxpayers more than $100,000 in the first year, and may be seen
             as giving the Republicans an unfair electoral advantage.

The colon, we have seen, is not used in syndetic coordination, and in aysndetic combinations it indicates an elaborative rather than coordinative interpretation. What it elaborates on may be a whole clause, as in [i], or a smaller element, such as his preference in [ii] or the non-final NP the rules in [iii]; indeed, there may be more than one such item, as in [iv], where the clause following the colon elaborates on both the costs and the political consequence.

Like the comma and semicolon, the colon can separate a positive-negative sequence, where the first clause contains not + only/simply/merely/just:

[19] The Romans built not only the Fort of Othona: they had a pharos, or lighthouse,
         on Mersea.

This does not invalidate our statement that the colon cannot be used to separate clauses in a coordinative relation. It is, rather, that the elaboration relation makes perfect sense in this context: the second clause provides an explanation or demonstration of what is said in the first clause. Note, then, that it would be quite impossible to insert but after the colon.