The connective のに (used in Ｓ１のに、Ｓ２ structure) was briefly introduced in Lesson 24 in its Grammar Notes (24.2). It expresses a contradiction between S1 and S2 ("Despite S1, S2"). のに is preceded by a whole sentence (typically in the plain form) as shown below. If S1 is a noun sentence or な-adjective sentence, な has to be inserted before のに.

• 電気はついているのに、ドアが開(あ)かないんだよ。 [Vのに]
  "Despite that the light is on, the door won't open."
  
  
• 今日は日曜日なのに、しごとに行くんです。[Nなのに or な-Adjなのに]
  "Despite that today is Sunday, I'm going to my work."
  
  
• あのレストランは安いのに、とてもおいしいんです。[い-Adjのに]
  "That restaurant is cheap, and yet (the food) is so delicious."

のに is commonly used at the end of counterfactual statements as shown below. The whole expression in (A) means "I wish..." (Lit. "It would be good if ..., but...").

A:	明日は雨がふったらいいのに…	I wish it would rain tomorrow.
B:	どうして？	Why?
A:	そうしたら、マラソン大会がないから…	If that is the case, we won't have a race.

Conditional Ｖたら (+ いい) creates a suggestion form "Why don't you V?" (LIt. "It would be good if you V...")

• あそこのATMから、お金(かね)を出(だ)したら？
  "Why don't you get the money out of that ATM?"
  
  
• わからなかったら、先生に聞いたらいいですよ。
  "If you don't understand, why don't you ask your teacher?"