Part 1
Periodic signal Sampling the signal at a frequency that is a rational multiple of the frequency of the signal will result in a periodic Discrete Time signal. Sampling the signal at a frequency that is not a rational multiple of the frequency of the signal will result in a non-periodic Discrete Time signal.
My all time favorite CT periodic signal- Sin(t)
t = 0:0.02:10; x = sin(t); plot(t,x) grid on
Periodic signal turned Non-Periodic, DT non-periodic signal
t = 0:0.5:10; x = sin((1/(2*pi))*t); plot(t,x) grid on stem(t,x)
Part 2
Non-Periodic Signal and Non-Periodic Signal turned Periodic
Using x(t) = t
Using image from Jacob Pfister.