15 terms

Consider the following partial grade book for a certain class.

Name | Exam 1 Score

-------------------------

Bill | 70

Gene | 83

Jesse | 86

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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)}.

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 = {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 = {0,2,4} 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 = {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 = {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 = {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 = {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)}

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 = {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 ]

[ 0 0 0 ]

0 1 1

[0 1 1 ]

True

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

Consider the following partial table of employee names, employee identification (ID) number, department, and age.

What would be the primary key?

What would be the primary key?

Employee ID

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

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.

[ 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)}

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