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They have two sons who became doctors.
They have two sons, who became doctors.

I think these two sentences have a different meaning. The first one means that they might have more than two children. So they have two sons who became a doctor and at the same time they might have one son who became a lawyer.
However, the second one means that they have only two sons and the sons are doctors.

Then, how about this sentence?

My family is four; we have two sons who are students.

Is "COMMA" obligatory between 'two sons' and 'who'?

According to the sentence, my family consists of four members. "We" might be mom and papa. Therefore, "We" must have two children, not more than two.

Please help me!!
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They have two sons who became doctors.

They have two sons, one of whom became a doctor.

I would not usually put a comma in the first sentence unless "who became doctors" was less important than the subsequent statement. (Sorry, I don't know the correct grammatical term).

Here's an example:

They have two sons, who became doctors, in the hospital at Birmingham.

Notice that the commas are essential here because they govern the meaning. In the previous sentence, the two sons became doctors somewhere unspecified. This is quite different from:

They have two sons, who became doctors in the hospital at Birmingham.
Comments  
Dear Reshary,

Sentence number two is not possible. It is: «they have two sons, who became doctors».

Kind regards, Emotion: smile
Goldmund
 Eimai_Anglos's reply was promoted to an answer.