Recall the general solubility rules for ionic compounds in water, which help predict whether a compound will dissolve or remain solid.
Identify the solubility of each compound in the given pairs based on these rules: for example, most sulfates (SO\_4^{2-}) are soluble except those of Pb^{2+}, Ba^{2+}, and Sr^{2+}.
Check the solubility of phosphates (PO\_4^{3-}), which are generally insoluble except those of alkali metals and NH\_4^{+}.
Evaluate each pair: PbSO\_4 and Pb\_3(PO\_4)\_2 both contain ions known to form insoluble salts, while the other pairs contain ions that typically form soluble compounds.
Conclude that the pair containing PbSO\_4 and Pb\_3(PO\_4)\_2 is insoluble in water based on these solubility rules.