1. They are very happy.

2. They are on cloud nine.
3. They are walking on air.
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Are they all the same in meaning? What is the meaning of 'air' in Sentence 3?

I think google is very helpful for these idioms. You can get various definitions and explanations.

Yes, all mean the same thing. You could also say, "They are ecstatic."

Walking on air is figurative language for being so happy, it's as if the person's feet aren't even touching the ground. It's just about the same as "on cloud nine."

Remember, these are expressions and idioms that have developed over a long period of time. They are not always able to be defined literally!

While sentences 1, 2, and 3 convey the same overall idea of happiness, they use different idiomatic expressions to describe it.

In sentence 1, "They are very happy," the meaning is straightforward. It indicates a high level of happiness without any metaphorical language.

Sentence 2, "They are on cloud nine," is an idiomatic expression. It means that someone is extremely happy or joyful. The phrase "cloud nine" is a metaphorical way of expressing the feeling of being elated or on top of the world.

Sentence 3, "They are walking on air," is also an idiomatic expression. Here, the word "air" is used metaphorically. The phrase means that someone is feeling elated or euphoric, as if they are walking lightly or with a spring in their step. The idea is that they are so happy that it feels like they are floating or walking on something light and airy.

So, the meaning of "air" in sentence 3 is not literal; rather, it represents the sense of lightness and euphoria associated with happiness.