だいmarks wh-question (what, where, who), strengthens one's judgment or conclusion

父(ちち)：「あの人(ひと)は誰(だれ)だい？」子(こ)：「担任(たんにん)の先生(せんせい)だよ。」

Father: "Who is that person?" Child: "That's our homeroom teacher." {marks wh-question (what, where, who), strengthens one's judgment or conclusion}

少年(しょうねん)：「僕(ぼく)がアイツを好(す)きだって？そんな噂(うわさ)は嘘(うそ)だい！」

Boy: "Me liking that guy? Such rumors are false!" {marks wh-question (what, where, who), strengthens one's judgment or conclusion}

生徒(せいと)が先生(せんせい)に：「先(さき)に殴(なぐ)ったのはアイツだ。アイツが悪(わる)いんだい！」

The student said to the teacher: "He was the one who hit first. It's his fault!" {marks wh-question (what, where, who), strengthens one's judgment or conclusion}

父親(ちちおや)：「何(なに)をしているんだい？」娘(むすめ)：「泥(どろ)まみれになった犬(いぬ)を洗(あら)っているのよ。」

Father: "What are you doing?" Daughter: "I'm washing the dog that got covered in mud." {marks wh-question (what, where, who), strengthens one's judgment or conclusion}

弟(おとうと)：「お姉(ねえ)ちゃんがいけないんだい！」姉(あね)：「違(ちが)うでしょ！あなたがいけないのよ！」

Brother: "It's your fault, sister!" Sister: "No, it's not! It's your fault!" {marks wh-question (what, where, who), strengthens one's judgment or conclusion}