1. (10 points) Sets: Write a formal description of the set containing the string aba. 2. (10 points) Sequences and Tuples: What is the power set of B={x,y} which is logically equivalent to the Boolean expression below: (PQ) 4. (15 points) Relations: Give a relation that is Symmetric and Transitive, but not Reflexive. 5. (15 points) Graphs: Is the statement "For every natural number n1 there exists a directed graph of n vertices for which every vertex has an indegree equal to its outdegree" TRUE or FALSE? 6. (15 points) Strings and Languages: For alphabet ={a,b,c}, suppose x and x=5. Give a string x that is a substring of x and has the following property: Among all substrings of x,x is both a prefix of x and a suffix of x, and is the longest substring of x. 7. (30 points) Proofs: Prove by induction on n that Cn=i=1ni3=41n2(n+1)2,nN