Texas A&M University-Corpus Christi / Dept. of Computing and Mathematical Sciences

MATH 2305 §002 -- Discrete Mathematics I -- Spring 2003

Chapter 3 Study Questions

Section 3.1 Sets -- Name:

  1. A set is formally defined as a collection of objects.
  2. Capital letters are used to denote sets and lower case letters to denote objects which may or may not be an element of a set.
  3. All elements of an infinite set can be listed.
  4. One way to describe a set is to describe a property that characterizes the set elements.
  5. The empty set is a subset of every set.
  6. The union of two sets is a subset of each of the two sets.
  7. Sets can be members of sets.
  8. The set A^3 means the set consisting of the cube of the set of elements of A.

 

Section 3.2 Counting-- Name:

  1. Counting often boils down to finding out how many members there are in a finite set.
  2. The multiplication principle only applies to two different events.
  3. Applying the multiplication principle can be done with or without repetition.
  4. The addition principle applies when the events have no common outcomes.
  5. Finding the number of four digit numbers that end with a 4 or 5 requires both the addition and multiplication principles.
  6. Counting can still be done systematically where the multiplication principle does not apply.

 

Section 3.3 PigeonHoles; Inclusion/Exclusion -- Name:

  1. Knowing the number of elements in each of two sets and the union of those two sets, you can find the number of elements in the intersection of the two sets.
  2. Venn diagrams can illustrate the Principle of Inclusion and Exclusion.
  3. Venn diagrams can even illustrate the Principle of Inclusion and Exclusion for more than three sets.
  4. In the formal statement of the pigeonhole principle, the bins correspond to pigeons and items to pigehonholes.
  5. There are 50 odd integers between 1 and 99 inclusive.

 

Section 3.4 Permutations and Combinations -- Name:

  1. The number 1259 is a permutation of 2951.
  2. In finding P(7,3), it is necessary to find the value of 7 factorial (7!).
  3. Counting permutations is just a formal way to use the multiplication principle.
  4. If order matters, its a permutation problem; if not, its a combination problem.
  5. Counting ways to form a committee in a club is a permutation problem, while choosing officers in the club is a combination problem.
  6. The letters S that appear in the word MISSISSIPPI are indistinguishable.
  7. The number of ways of selecting r out of n distinct objects with repetitions allowed is C(r+n-1,r).

 

Section 3.5 Probability I -- Name:

  1. For all dice, the probability of rolling a 3 with a single roll is 1/6.
  2. There are 4 elements in the sample space for the tossing of two coins.
  3. Determining the number or elements in a sample space can require counting.
  4. The probability of an event is the ratio of the sizes of two sets.
  5. Probabilities of individual outcomes must always be identical to the probability of every other individual outcome.
  6. The sum of the probabilities of individual outcomes is 1.

 

Section 3.5 Probability II -- Name:

  1. In Example 65, if you know that a patient responded positively to compound A, then he or she is more likely to respond to compound B that a patient you don't know anything about.
  2. The probability of an intersection is the product of the probabilities of the sets forming the intersection.
  3. A function that assigns a numerical value to each outcome in a sample space is called a random function.
  4. The expected value of a random variable is a weighted average.
  5. Analyzing algorithms requires considering every possible case the algorithm might undertake.