# CS 173, Fall 2014: Skills list for twelfth examlet

• Logic and proofs
• Recap from the past: give the negation of a statement or the contrapositive (if/then statements only), simplifying it so that all negations are on individual propositions/predicates.
• Write a proof by contradiction.
• Collections of sets
• Manipulate sets containing other sets using standard set operations. (Be careful of getting the right number of brackets in examples involving the empty set and sets with only one element.)
• Define the power set P(A) for a set A.
• Given a specific set A, list the elements of its power set.
• Correctly interpret set-builder definitions of sets containing other sets.
• Correctly interpret definitions for functions whose input and/or output values are sets.
• Write simple proofs involving collections of sets, functions whose input and/or output values are sets.
• Partitions
• Define a partition of a set A.
• Determine whether a specific set is a partition of some specific set A.
• Know that the equivalence classes of an equivalence relation form a partition.
• Counting
• Know the shorthand notation for binomial coefficients (number of combinations) and its definition in terms of factorials.
• Know the formula for computing the number of combinations of k objects from n types, with repetition.
• Know the Binomial Theorem and Pascal's Identity
• Be able to solve practical counting problems involving combinations, combinations with repetition, and applications of the Binomial Theorem.