Let A be a regular set. Consider the two sets below L1={x | $\exists n\geq 0, \exists y\epsilon A :$ y=$x^n$} L2={x | $\exists n\geq 0, \exists y\epsilon A :$ x=$y^n$} which of the following statements is true? L1 and L2 both are regular L1 is regular but L2 is not L1 is not regular but L2 is L1 and L2 both are non-regular

Consider the infinite two-dimensional grid $G=\{(m,n)|\text{m and n are integers} \}$ Thus every point in G has 4 neighbours, North, South, East and West, obtained by varying m or n by $\pm 1$. Starting at origin (0,0), a string of command letters N, S, E, W generates a path in G. For ... $L'$ is context free A. 1,2 and 3 only B. 3 and 4 only C. 4 only D. 1 and 2 only