The assertion [a] is true. Polyester POY (Partially Oriented Yarn) typically shows higher shrinkage in boiling water compared to polyester FDY (Fully Drawn Yarn), as POY has less molecular orientation.
However, the reason [r] is false. In fact, polyester FDY has a higher level of molecular orientation than POY due to the higher drawing process involved in its production. This higher orientation leads to better dimensional stability, which results in lower shrinkage during boiling.
Thus, while [a] is correct, [r] is incorrect as the explanation for [a].
Final Answer: The correct answer is \( \boxed{D} \).