Let x(t) be a continuous-time signal, and let

                                               y₁(t) = x (2t) and y₂(t) = x(t/2).

The signal y₁ represents a speeded up version of x(t) in the sense that the duration of the signal is cut in half. Similarly, y₂(t) represents a slowed down version of x(t) in the sense that the duration of the signal is doubled.

Consider the following statements :

   (1) If x(t) is periodic, then y₁(t) is peiodic.
   (2) If y₁(t) is periodic, then x(t) is peiodic.
   (3) If x(t) is periodic, then y₂(t) is peiodic.
   (4) If y₂(t) is periodic, then x(t) is peiodic.

For each of these statements, determine whether it is true, and if so, determine the relationship between the fundamental periods of the two signals considered in the statement.

If the statement is not true, produce a counterexample to it.