The reactions are as follows:
\[
\text{Cl}_2 + \text{NaOH (aq)} \rightarrow \text{NaCl} + X + \text{H}_2\text{O} \quad \text{(reaction 1)}
\]
\[
\text{Cl}_2 + \text{NaOH (aq)} \rightarrow \text{NaCl} + Y + \text{H}_2\text{O} \quad \text{(reaction 2)}
\]
In reaction 1, chlorine undergoes a reduction to form chloride ion (\( \text{NaCl} \)), and X has an oxidation state of +1.
In reaction 2, chlorine undergoes oxidation to form a species Y, where chlorine has an oxidation state of +5.
Thus, the oxidation states of chlorine in X and Y are \( +1 \) and \( +5 \) respectively.