After a war, could the men of Israel take a woman of the captives as a wife? If no, why not? If yes, how?
According to Jewish law (Deut 7:3-4): No.
In Deuteronomy 21:10-13: Yes.
We are having a little disagreement in our Bible studies class. Which scripture correctly answers the above mentioned question?
Both scriptures correctly answer the question, "After a war could the men of Israel take a woman of the captives as a wife?" The correct answer, based on the two scriptures you mention, is "it depends on who was conquered."
In Deuteronomy 7:1-4 (to get the whole context), the Israelites were forbidden to marry a woman captive of one of seven nations: the Hittites, and the Girgashites, and the Amorites, and the Canaanites, and the Perizzites, and the Hivites, and the Jebusites. The law in Deuteronomy 21 applies to any other nation. So the Israelites were forbidden to intermarry with the nations they were supposed to be expelling from Canaan, but once that occupation was accomplished they could marry captives of other nations, such as the Philistines and the Moabites. Thus, it was not wrong for Boaz to marry Ruth the Moabitess (Book of Ruth), because she was not from one of the forbidden nations.