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Consider that the relation has only one attribute $A$.

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I could also translate the RA query into an equivalent SQL query. I assume the working should still hold.
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@shashin, Yes I agree that we can translate RA to sql.

But as far as I know RA query only takes relation as input and gives relation as output and this relation is set of tuples.

So I thought that relation should not include any duplicate.

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@Vimal Patel - does this help ?

https://www2.cs.sfu.ca/CourseCentral/354/zaiane/material/notes/Chapter4/node11.html

• Formal query languages are based on mathematical relations. Thus no duplicates appear in relations.
• As duplicate removal is expensive, SQL allows duplicates.

Here we are just told 'relations' - so we assumed a practical implementation that mostly allows duplicates. From a purely mathematical perspective - no duplicates. What say ?

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first line itself says "Formal query languages are based on mathematical relations. Thus no duplicates appear in relations."
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Btw this is such a little detail that we should not debate over it. :)

I just thought that you guys have mistakenly missed it. But you have not.