Understand that an oxidation-reduction (redox) reaction involves the transfer of electrons, where one species is oxidized (loses electrons) and another is reduced (gains electrons).
Examine each reaction to identify changes in oxidation states of the elements involved.
For the reaction \(\mathrm{Zn + Cu^{2+} \rightarrow Zn^{2+} + Cu}\), note that zinc goes from 0 to +2 (oxidation) and copper goes from +2 to 0 (reduction), indicating electron transfer.
For the reaction \(\mathrm{HCl (aq) + NaOH (aq) \rightarrow NaCl (aq) + H_2O (l)}\), recognize this as an acid-base neutralization with no change in oxidation states.
For the reactions \(\mathrm{CaCO_3 (s) \rightarrow CaO (s) + CO_2 (g)}\) and \(\mathrm{NaCl (aq) + AgNO_3 (aq) \rightarrow AgCl (s) + NaNO_3 (aq)}\), check that oxidation states remain constant, indicating no redox process.