Part 1
Choose the signal $ x(t)=cos(t) $ which is periodic.
Sampling ever interger yields
This is $ x[n]=cos(n) $
but sampling at a frequency of $ \pi/4 $ yields
This is $ x[n]=cos(\pi/4n) $
Part 2
chooseThis is $ x(t) $
Choose the signal $ x(t)=cos(t) $ which is periodic.
Sampling ever interger yields
This is $ x[n]=cos(n) $
but sampling at a frequency of $ \pi/4 $ yields
This is $ x[n]=cos(\pi/4n) $
This is $ x(t) $