• From the catalog: Sets, relations, functions, sentential and predicate logic, proof techniques, algorithms, and elementary metatheory. Mathematically oriented. Prerequisite: Three years of high school mathematics. Three lecture hours and one laboratory hour a week for one semester.

• Note: This course is required of computer sciences majors. Typically, few except computer sciences majors take this course.

• We will closely follow the text of Robert L. Causey, Logic, Sets, and Recursion, Second Edition, 2006, Jones and Bartlett, ISBN 0-7637-3784-4. 512+ix pages. NOTE: this is the second edition, not the older revised edition with supplement. We will proceed through the Causey text in the order of the Table of Contents, leaving off some sections at the ends of some chapters. Thus the order of study is Sentential Calculus, Set Theory, Number Theory, and finally Predicate Calculus.

• Here is a syllabus recommended by the computer sciences department, one that I try to cover, though not in this exact order.

  
    Logic
      propositional connectives
      truth tables
      satisfiability
      validity
      provability
      tautologies 
      quantifiers
  
    Sets
       elements
       subsets
       union, intersection, set difference 
       cartesian product
       cardinalities of finite sets
  
    Relations
      reflexivity, symmetry and transitivity
      equivalence relations and partitions
      composition
  
    Functions
      1-1
      onto
      invertibility
  
  
    Induction
      its use for proving simple numerical identities 
        and for defining functions
  
  

Here is a more detailed syllabus for the course, together with many example problems, courtesy of Prof. Elaine Rich of the Computer Sciences Department. The course should enable you to solve these sorts of problems.

P. S. The University of Texas has many rules and regulations. It is highly recommend that for all courses at the University of Texas that students be familiar with the General Information catalog, the Course Catalog, and of course the Course Schedule, which can all be found on-line at http://www.utexas.edu. Also highly recommended is http://cns.utexas.edu/faculty/files/2006CourseworkRoutine.pdf , Dean Laude's memo on Coursework and Routine: Policies, Procedures, and Recommendations.