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why don't we use the projection operator in conditional join?

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Conditional Join is also known as theta join. It combines tuples from different relations provided they satisfy the theta condition.

Ex: R1 and R2 are relations having attributes (A1,A2...An) and (B1,B2,….Bn) such that attributes don’t have any thing in common, that is R1 (intersection) R2 = pie.

since there are no common things, there are no duplicates, without duplicates there is no use of using projection operator.

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