In Column-$I$ processes and in Column-$II$ the first law of thermodynamics are given. Match them appropriately:

Column-$I$	Column-$II$
$(a)$ Adiabatic	$(i)$ $\Delta Q = \Delta U$
$(b)$ Isothermal	$(ii)$ $\Delta Q = \Delta W$
	$(iii)$ $\Delta U = -\Delta W$

(A) The first law of thermodynamics is given by $\Delta Q = \Delta U + \Delta W$.
$(a)$ For an adiabatic process,there is no heat exchange with the surroundings,so $\Delta Q = 0$. Substituting this into the first law: $0 = \Delta U + \Delta W$,which implies $\Delta U = -\Delta W$. Thus,$(a)$ matches $(iii)$.
$(b)$ For an isothermal process,the temperature remains constant,which implies the change in internal energy $\Delta U = 0$. Substituting this into the first law: $\Delta Q = 0 + \Delta W$,which implies $\Delta Q = \Delta W$. Thus,$(b)$ matches $(ii)$.
Therefore,the correct matching is $(a-iii), (b-ii)$.