When a nucleus with atomic number Z and mass number A undergoes a...

- (A) both Z and A will decrease if the process is a-decay: True. In a-decay, a nucleus emits an alpha particle ($_2^4$He), so Z decreases by 2 and A decreases by 4. - (B) (\mathrm{Z}) will decrease but $A$ will not change if process is (\beta^{+})decay: True. In (\beta^{+})decay (positron emission), a proton converts to a neutron, emitting a positron ($_1^0$e). So Z decreases by 1, and A remains unchanged. - (C) (\mathrm{Z}) will decrease but (\mathrm{A}) will not change if process is (\beta) - decay: False. In (\beta) - decay (electron emission), a neutron converts to a proton, emitting an electron ((_{-1}^{0} \mathrm{e})). So Z increases by 1, and A remains unchanged. - (D) Z and A will remain unchanged if process is y-decay: True. Gamma decay involves the emission of a high-energy photon (gamma ray) from an excited nucleus, which only de-excites the nucleus without changing its atomic number (Z) or mass number (A). The correct statements are (A), (B), and (D). This corresponds to option (4).