# Recent questions tagged virtual-gate

1
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
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3
Which one of the following languages over the alphabet ${0, 1}$ is regular$?$ $(A)$ The language of balanced parentheses where $0, 1$ are thought of as $(,)$ respectively $(B)$ The language of palindromes, i.e., bit strings $x$ that read the same from left to right as well as right to ... $(D)$ The kleene closure $L^{*},$ where $L$ is the language in $(C)$ above Ans is $D$ please explain$?$
4
If both x and y are integers, then the point P(x,y) is called a lattice point of the plane. Suppose Pi, 1 <= i <= 5, are five (different) lattice points. We form a complete graph using these 5 points and the unique straight line segments (edges) determined by the ... edge) as a lattice point is: 1 2 3 4 Explain what they are asking and then the solution. I am not able to understand question also