For linearity
y1[n] = x1[n] + x2[n - 10] ...(1)
y2 = x2[n] + x2[n - 10] ...(2)
y1[n] = x1[n] + x2[n] + x2[n - 10] + x2[n - 10] ...(3)
Now find y1[n] + y2[n]
Corresponding to x1[n] + x2[n]
It is same as equation (3) hence linear.
But in part (c) y[n] = x2[n]
⇒ y1[n] = x21[n], y2[n] = x22[n]⇒ y1[n] + y2[n] = x22[n]...3
But y1[n] + y2[n]
Corresponing x1[n] + x2[n] is y1[n] + y2[n] = {x1[n] + x2[n]}2
= x12[n] + x22[n] + 2x1[n] x2[n]....4
Equations (3) and (4) are not same hence not linear.
