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.