Let \(f\) and \(g\) be periodic functions with the periods \(T_{1}\) and \(T_{2}\) respectively. Then \(f+g\) is
(A) periodic with period \(T_{1}+T_{2}\)
(B) non-periodic
(C) periodic with the period \(\mathrm{T}_{1}\)
(D) periodic when \(\mathrm{T}_{1}=\mathrm{T}_{2}\)