What is the Nyquist theorem?

The frequency which, under the sampling theorem, must be exceeded by the sampling frequency is called the Nyquist rate. Determine the Nyquist rate corresponding to each of the following signals: (a) x(t)=1+cos (2,000 π t)+sin (4,000 π t) (b) x(r)=(sin (4,000 π t))/(π t) (c) x(t)={ .(sin (4,000 π t))/(π t))^2 .