Hi, I need some help correcting my answer for a discreet math problem, as my professor mentioned that it was incorrect. First, let me state the problem:

Second, let me state the answer that I gave along with the reasoning: The strings that have a length of 3 or less which can be constructed from the alphabet are: x, y, xx, yy, xy, yx, xxx, yyy, xxy, xyy, xyx, yxx, yyx, yxy. Since the next parameter requires that we select strings in which xs appear to be to the left side of the ys, we get: L₃= {xy, xxy, xyy} My professor stated that the answer I gave (above in bold) is incomplete, because I also needed to include strings of only x's and only y's since in those strings the requirement for all x's in the string being to the left of all y's in the strings also holds. So that being said, would this answer be correct? L₃= {x, y, xx, xy, yy, xxx, xxy, xyy, yyy} If not, what would be the correct answer, and why? Thanks for helping me to understand this.

Let 2 - [x,y] be an alphabet a) Let Ls be the language consisting of all strings over of length S 3 in which all the x's appear to the left of all the y's. List the elements of L3 between braces. Let 2 - [x,y] be an alphabet a) Let Ls be the language consisting of all strings over of length S 3 in which all the x's appear to the left of all the y's. List the elements of L3 between braces