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Two aldopentoses \( \mathrm{X} \) and \( \mathrm{Y} \) give the same osazone derivative. \( \mathrm{X} \) is oxidised to an optically active aldaric acid by dilute nitric acid. Ruff degradation of \( Y \) gave a tetrose which was similarly oxidised to an optically active aldaric acid. Assign the structures of \( \mathrm{X} \) and \( \mathrm{Y} \) from the following list.
(I)
(III)
(a) \( \mathrm{X}= \) (I) and \( \mathrm{Y}= \) (III)
(c) \( \mathrm{X}= \) (II) and \( \mathrm{Y}=(\mathrm{IV}) \)
(II)
(IV)
(b) \( \mathrm{X}= \) (IV) and \( \mathrm{Y}= \) (II)
(d) \( \mathrm{X}= \) (III) and \( \mathrm{Y}=(\mathrm{I}) \)
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