The correct option is C Michael can take up science or economics next year.
A compound sentence is made up of independent clauses that can stand on
their own as sentences. Alternative compound sentences express a choice
between two alternate choices, like in the given sentence. When the given sentences are connected, 'or' is the most suitable option as it presents the choice between science and economics. The subject is common between both sentences, it refers to the same person, hence it can appear once in the combined sentence. Option C contains the correct form of the combined sentence, with the second clause being an elliptical sentence, i.e., a shortened version of the original sentence, as the meaning is already implied. Hence C is correct. Option A is grammatically correct, but repeating the words 'next year' is not required and the resulting sentence doesn't sound natural, hence A is incorrect. Option B has changed in meaning, making the choice between the words 'can' and 'take', and adding the cumulative conjunction 'and'; hence it's incorrect. Similarly, D has a misplacement of the conjunction 'or', presenting the choice between 'take up' and 'science and economics', hence D is also incorrect.