Periodicity of discrete function

Question

Let $x[n]$ a discrete-time signal, $$y[n]= x[2n]$$

I have seen that if $x[n]$ is periodic then $y[n]$ is periodic. Similarly, can we say that if $y[n]$ is periodic then $x[n]$ is periodic as well. Why, why not ?

Answer 1

You can't say anything.

Suppose you have the signal $y[n] = 1$, it's periodic

Now you have the signal $x[2n] = 1$ and $x[2n+1] = n$. You have $x[2n] = y[n]$ but $x$ is not periodic