Module 9 Worksheet
In Class Questions
1) (S6) Give an element of FINITE over alphabet {a,b,c}.
2) (S6) Give an element of FINITE over alphabet {a,b,c} that is NOT in CARD-3.
3) (S7) Does the example on this slide prove that FINITE is closed under set union?
4) (S11) What is k for the set union operation?
What is k for the set complement operation?
5) (S12) True or false. Since we can write all of these closure properties as first-order
logic statements, they all must be true. Explain your answer.
Take home review questions
1) What does it mean if I say that a set S is closed under binary operation O?
2) Is the set of finite languages closed under the concatenation operation?
3) What do I mean when I say that a closure property often represents an infinite set of
facts, and why does this make first-order logic helpful in formally writing closure
property statement?