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

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

Chapter 4 Study Questions

Section 4.1 Relations -- Name:

1. A binary relation on a set S is a subset of the set S.
2. Relations can be one-to-one, one-to-many, many-to-one, or many-to-many.
3. The property of relations that says every x is related to itself is the reflectory property.
4. Partial orderings can be displayed in a Hasse Diagram.
5. Every binary relation partitions a set into subsets called equivalence classes.
6. Every integer is congruent modulo 4 to one of the following: 0,1,2,3.

Section 4.4 Functions-- Name:

1. The association made by functions can be described by ordered pairs.
2. The set of starting values for a function is called the domain and the set from which the associated values come is the codomain.
3. A function is a special kind of binary relation.
4. The domains and codomains of functions must be sets of numbers.
5. The ceiling function associates with each real number x how far the number is from the smallest integer greater than or equal to it.
6. To show a function is one-to-one, assume that x1 = x2 and show f(x1) = f(x2).
7. The composition of two functions is a new function.
8. The composition of two permutations is a permutations.
9. There are 6 functions with domain {A,B,C} and codomain {a,b}.
10. The functions f(x) = 3x^2 and g(x) = 200x^2 + 140x +7 have the same order of magnitude.

Section 4.4 Matrices-- Name:

1. In Example 46, the entry in the 2nd row and 5th column of the matrix A is 44.
2. The main diagonal entries of the matrix A in Example 50 are [1,0,6].
3. Any two matrices can be added together.
4. The multiplicative identity matrix (designated by I) has all entries equal to one.
5. If /\ represents boolean multiplication, then 1 /\ 0 = 1.