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I can't really tell the exact differences between them.

1. I saw the news on TV.

> I saw the news on TV meself. I payed attention to it.
2. I read the news on TV.

>This sentense sounds strange for my ears. I would say I read the news in the newspapers.
3. I heard the news from the news channel. ==> I heard the news, meaning you might just happen to hear it while you were occupied by something else, you didn't really focus 100% on the news.

Am I correct?
Comments  
When we say that we have "seen" a piece of news, this implies that we saw it on television (or, these days, the internet).

If someone says that they "read" the news, this implies that the source was a newspaper, magazine, or the internet.

News that we "hear" can come from any source. When we say that we have "heard" certain news, or that we have "heard about" something, we are speaking generally about some recent piece of information that we have learned from somewhere. We might have seen it on TV, heard it on the radio, read about it, or have been told of it by another person.

We wouldn't say that we had "read" something on TV, but news on the internet could be either "read" or "seen".

Whether a person says that they have read, seen or heard news tells us nothing about their level of concentration at the time. Other words would have to be added to convey this, for example:

I just happened to see the news about the accident while I was making dinner.
I’ve noticed that your answers are thoughtful and thorough. Thanks.
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Dave, Thank you very much for elaborated explanation. Here is my summary.

1. have 'seen' the news, this is usually associated with video or image, such as on TV or Internet.

2. When you read the news, the news are presented in a form of words, such as in print media or Internet (text only)

3. When you hear something, it can be from any source but from aurally transmission.

I just happened to see the news about the accident while I was making dinner. (OK)
I just happened to hear the news about the accident while I was making dinner. (OK)
I just happened to read the news about the accident while I was making dinner. (Not OK, I think the action of reading clashes with making dinner. But i'm wondering that one person might be very capable for he can do two things perfectly at the same time.)

I'm looking forward to your answer.
I agree with statements [1] and [2].

I'd like to comment further on statement [3]. When people speak of having "heard" something, they may not literally mean that the information was aurally transmitted. Example:

A: Have you heard the latest news about Iraq?
B: Yes, I think everyone's heard about it.

Notice that the speakers haven't specified any particular news source. They are speaking generally, and are using the verb "hear" to include news received from any source.

As for reading the news while making dinner, I agree that this would be difficult, though, I suppose, not impossible. It's certainly a less likely sentence than the two other examples you have given.
Hi ,
I read the news to me sounds like a radio talkshow host reads the news to the listeners.
I see the news on tv is more correct than I read the news on tv. Becasue unless you watch channel like cnn that they have additional news in words running at the bottom of the screen such as sports while you watch a person or people talk about other news at the same time.

Am I correct?
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Yes, you are correct.
Any subtitles or captions that run around on the screen is a good example of 'reading the news' as well.
Thank you, David. It's cevry clear now.