Why doesn't sampling a periodic continuous-time signal yield a periodic discrete-time signal?

I have been studying signals and systems lately and I have came across the following claim:

The uniform sampling of a periodic continuous-time signal may not be periodic!

Can someone please explain why this statement is true?

• Correct me if i am wrong: But when the input singal is 1kHz and you sample with 3.5kHz, you get a periodic signal with a period time of 2ms. To get a periodic signal, f_s does not need to be n*f_in but can be n*f_in/m – 12431234123412341234123 May 22 at 10:44