Should the highlighted commas be present in the following sentences?
- If he arrives, his girlfriend will be happy(,) but I will have to prepare another place at the table.
- If her hypothesis is true(,) and his theory is right, then the experiment should be successful.
- Since this is a set of natural numbers(,) and no natural number is negative, it is clear that its sum must be positive.
- Therefore, the theorem is true because the preceding expression is positive(,) and the second lemma guarantees that so is its factorial.
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