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Hi,
I think the extreme example of perfect elastic demand and supply is unlikely to come up on the exam (as I have not seen it described in the curriculum). In theory if both supply and demand is perfectly elastic then no transactions would take place unless both supply and demand was perfectly elastic around the exact same price point, in which case there would be no deadweight loss. But I really do not think you need to worry about this question coming up on the test.
I would focus on understanding how the share of the burden from a tax is distributed on the buyer/seller depending on the relative elasticity of the demand/supply. The group (buyer/seller) with the steepest (less elastic) curve will suffer disproportionally from a tax irrespective if it is imposed on the buyer or seller.