The Torah repeats the prohibition of boiling a kid (a baby goat) in its mother's milk three times. From the repetition we conclude that the prohibition applies to other animals' meat and milk, and to eating the result, not just to the cooking itself. "Boiling" includes all types of cooking, "meat" includes all edible body parts of the animal, and "milk" includes milk products. If meat and dairy ingredients were cooked together, the result is Biblically forbidden. In any case, the Rabbis forbid eating meat products and milk products together even if they weren't cooked together.
The Torah doesn't give a reason for the meat/milk prohibition. Maimonides suggests that eating such mixtures was associated with idol worship.
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