Step 1: Understanding the oxidation state of oxygen in H\(_2\)O\(_2\).
In hydrogen peroxide (H\(_2\)O\(_2\)), oxygen has an oxidation number of –1, because the total oxidation state of hydrogen is +2 and the molecule is neutral.
Step 2: Understanding the oxidation state of oxygen in H\(_2\)O.
In water (H\(_2\)O), oxygen has an oxidation number of –2, as the total oxidation state of hydrogen is +2 and the molecule is neutral.
Step 3: Conclusion.
Thus, the oxidation numbers of oxygen in H\(_2\)O\(_2\) and H\(_2\)O are –1 and –2, respectively, which corresponds to option (A).