CS 420/520 Theory of Computation, Spring 2019 at Indiana State University, taught by Jeff Kinne
Quiz 1 - Sipser chapter 0 exercises and proofs

Points - each part is graded as 1 point, either right or wrong, except that problem 4 counts as 3 points and can get partial credit.

** 1 - Sets **
Let A = {a, b}, B = {b, c, d}

1.0) What is A union B?

1.1) What is A intersect B?

1.2) What is A cross B?

1.3) What is the power set of B?

1.4) If A is a set with 100 elements, how many elements are in the power set of A?

1.5) If A and B are sets with 99 elements, how many elements are in A cross B?


** 2 - Functions and Relations **

2.0) What is the range of the function f(x) = x*x

2.1) Given a binary relation R, what does it mean for R to be symmetric?


** 3 - Graphs **

3.0) Draw a directed graph that has 4 vertices and 6 edges.

3.1) If a directed graph has 10 vertices, what is the highest number of edges it can have (count self-loops as edges as well)?


** 4 - Proof by induction **

Write a proof by induction that the following is true.  Or, if you don't like this one, state some other summation formula and prove it is true using induction.
Claim - The sum of the first k even positive integers is k * (k+1)