particle
although; despite; even though; whereas
Concessive particle expressing that something is contrary to expectation. Connects clauses where the result is unexpected given the preceding statement. Often carries a nuance of dissatisfaction or surprise.
雨が降っているのに、彼は傘を持っていない。
Although it's raining, he doesn't have an umbrella.
彼は若いのに、とても落ち着いている。
Despite being young, he is very composed.
particle
Used at the end of a sentence to express a wish or regret about something that is not the case. Often follows the conditional form ~ば or ~たら.
もっとお金があればいいのに。
If only I had more money.
早く夏休みにならないかなあ。なったらいいのに。
I wish summer vacation would come soon.
particle
Indicates purpose or use. Follows the dictionary form of a verb and is often used in explanatory or instructional contexts. Equivalent to ために in many cases.
この道具は、野菜を切るのに便利です。
This tool is useful for cutting vegetables.
駅に行くのにバスを使った。
I took the bus to go to the station.