Problem Set 3 Comments

Problem Set 3 comments are here: [PDF]

2 comments to Problem Set 3 Comments

  • Robyn Short

    I am having some trouble with question #5, parts b and c. I was thinking that these two problems could be solved visually with a venn diagram–is this approach valid? If so, how would it be done? I could not seem to make it work, but it seems like it should work, unless intersection here means something different than overlap in a venn diagram.

    • A Venn diagram might help you visualize what the closure properties mean, but it won’t be very useful in proving them.

      Remember that a language is a set of strings, and a language class is a set of languages. The intersection of two languages A and B is the intersection of the two sets, so we could draw this as two intersecting circles in a Venn diagram. The intersection is a new language, which is a point in the sets-of-languages diagram, but it doesn’t tell use where that point is. The questions 5b and 5c illustrate that this point need not be inside the same set as where A and B are.