Step 1: Understand the definition of an oxyanion. An oxyanion is a polyatomic ion that contains oxygen atoms bonded to another element (usually a nonmetal).
Step 2: Examine each ion given in the problem to see if it contains oxygen atoms bonded to another element:
- \(\mathrm{NO_3^-}\) contains nitrogen and oxygen atoms, so it is an oxyanion.
- \(\mathrm{SO_4^{2-}}\) contains sulfur and oxygen atoms, so it is also an oxyanion.
- \(\mathrm{NH_4^+}\) contains nitrogen and hydrogen atoms but no oxygen, so it is not an oxyanion.
- \(\mathrm{CN^-}\) contains carbon and nitrogen atoms but no oxygen, so it is not an oxyanion.