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If I understand your question correctly, i.e.

> Is it possible to enforce that constraint ***at the database level***?

Then the short answer is: No.

> In the business logic for the program, every record in the A table must have a relationship to at least one record in the B table

Since you already a `M:M` relation between tables A and B through an associative table C, you can only require that an entry in C already has valid PKs in tables A and B. However, there's no way (AFAIK) to cause entry in A to depend on an entry in B or vice versa , **unless** the relation between A and B is set to be 1:M. In other words, you'd have to go from:

```
+---+      +---+      +---+
| A |1----*| C |*----1| B |
+---+      +---+      +---+
```
to something like:
```
+---+          +---+
| A |*-----1..*| B |
+---+          +---+
```
where `*` by itself means "0 or more" and `1..*` means "1 or more".

If you want the above, but without changing the original M:M relation, you may need to look at either using database triggers (what I'd look into first) or implementing it in the actual application code (which I'd try to avoid).

If there's no choice but to write it in the application layer code, I'd at least put it in a library/module that can be easily reused across the entire application, to prevent this implementation issue from propagating uncontrollably; it is technical debt.