MTH-2215: Applied Discrete Mathematics: Quiz 3

Let A = {0,1,2} and R be the relation on A given by R = {(0,0),(0,1),(0,2),(1,2),(2,2)}. Is R antisymmetric?

Yes

Let A = {0,1,2} and R be the relation on A given by R = {(0,0),(0,1),(1,0),(2,2)}. Is R symmetric?

Yes

Let A = {0,2,4} and let R be the relation from A to A consisting of pairs (a,b), where a ≤ b. List all the pairs in R.

{(0,0),(0,2),(0,4),(2,2),(2,4),(4,4)}

Let A = {1,2,3} and B = {0,1,2,3}. If R is the ">" relation from A to B, list the pairs in R.

{(1,0),(2,0),(2,1),(3,0),(3,1),(3,2)}

Let A = {0,3,6,9}, and let R be the relation on A such that(a,b) ∈ R provided a | b, where a and b are both elements of A. List all pairs in R.

{(3,3),(3,6),(3,9),(6,6),(9,9),(3,0),(6,0),(9,0)}

Consider the matrix [ 1 1 0 ] 1 0 1 [ 0 0 0 ] representing a relation R on the set {x,y,z}. List all the pairs in this relation, where row/column 1 corresponds to x, row/column 2 corresponds to y, and row/column 3 corresponds to z.

{(x,x),(x,y),(y,x),(y,z)}

Consider the following partial table of employee names, employee identification (ID) number, department, and age. What would be the primary key?

Employee ID

Consider the following partial grade book for a certain class. Name | Exam 1 Score ------------------------- Bill | 70 Gene | 83 Jesse | 86 ------------------------- Consider the set A = {Bill, Gene, Jesse} and B = {0,1,... , 100}. Then consider the relation R from A to B consisting of pairs (a,b) from the table above with a ∈ A, b ∈ B. In listing all the pairs of R, we have {(70,Bill),(83,Gene),(86,Jesse)}.

False

Let A = {0,1,2} and B = {4,8,9}. Let R be the relation from A to B such that (a,b) ∈ R provided that ab = 8. Then all the pairs in R are {(8,1),(4,2)}

False

Let A = {1,2,7} and consider the relation R on the set A defined by R = {(1,2), (1,7), (7,1)}. In representing R using a digraph, there should be a directed edge from 2 to 1.

False

Let A = {0,1,2} and R be the relation on A given by R = {(0,0),(0,1),(0,2),(1,0),(1,2),(2,1),(2,2)}. Is R reflexive?

No

Let A = {0,1,2} and R be the relation on A given by R = {(0,0),(0,1),(1,0),(1,2),(2,1),(2,2)}. Is R transitive?

No

Let A = {0,2,4} and B = {0,1,2}. Let R be the relation from A to B of all ordered pairs of the form (a,b), where a is in A and b is in B, and where a/b is an integer. Then the pairs in R are {(0,1),(0,2),(2,1)(2,2),(4,1),(4,2)}

True

Let A = {1,2,3}, B = {2,3}, and C = {3,6}. Suppose R is a 3-ary relation that is defined by the following rule (a,b,c) is an element of R provided that a + 2 = b and b | c, and where a ∈ A, b ∈ B, and c ∈ C. Then the triples in R are {(1,3,3),(1,3,6)}.

True

Let A = {3,4,5}, and let R be the relation on A consisting of pairs of the form (a,b), where ab > 15, and both a and b are elements of A. If we represent R using a matrix (where the first, second, and third rows/columns of the matrix correspond to 3, 4, and 5, respectively), the matrix would be [ 0 0 0 ] 0 1 1 [0 1 1 ]

True