Consider the following problems related to the periodicity of discrete-time signals.

(a) Determine whether the following discrete-time sinusoids are periodic or not. If periodic, determine its fundamental period N₀.

(i) x[n]=2 cos(πn − π/2),                

(ii) y[n] = sin(n − π/2),

(iii) z[n] = x[n] + y[n],                     

(iv) v[n] = sin(3π n/2).

(b) Consider two periodic signals x₁[n], of fundamental period N₁ = 4, and y₁[n], of fundamental period N₂ = 6. What would be the fundamental period of

(i) z₁[n] = x₁[n] + y₁[n],  (ii) v₁[n] = x₁[n] y₁[n],     (iii) w₁[n] = x₁[2n]?