Assignment 7
(Select all that apply) Given the set {1, 2, 3} and the relation on that set, {(1, 2), (1, 3), (3, 3)} which of the following ordered pairs if added will make the relation reflexive?
(1,1) (2,2)
Which of the following are triples in the relation {(a,b,c) | a,b, and c are integers with 0 < a < b < c < 5}
(2,3,4) (1,2,3) (1,3,4) (1,2,4)
(Select all that apply) Given the set {1, 2, 3} and the relation on that set, {(1, 2), (1, 3), (3, 3)} which of the following ordered pairs if added will make the relation symmetric?
(3,1) (2,1)
Let R be the relation on the set {0, 1, 2, 3} containing the ordered pairs {(0, 1), (1, 1), (1, 2), (2, 0), (2, 2), (3, 0)} which of the following is the directed graph of the symmetric closure?
0 1 2 3 *First, figure out how to make the relation contain every symmetric ordered pair. (2, 0) -> (0, 2) (1, 2) -> (2, 1) (2, 0) -> (0, 2) (3, 0) -> (0, 3) Then include the new ordered pairs to the original relation and graph it.
Given the set {1, 2, 3} match the relation on the left with the corresponding matrix on the right. {(1, 3), (3, 1)}
0 0 1 0 0 0 1 0 0
Given the following set {1, 2, 3, 4} what is the resulting matrix if the relation is: {(1, 3), (2, 1), (2, 2), (2, 4), (3, 4), (4, 4)} (Use the fx button in editor to create a matrix.)
0 0 1 0 1 1 0 1 0 0 1 0 0 0 0 1
Given the set {1, 2, 3} match the relation on the left with the corresponding matrix on the right. {(1, 2), (2, 1), (2, 2), (3, 3)}
0 1 0 1 1 0 0 0 1
(Select all that apply) Which of the following zero-one matrices are equivalent relations?
1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 1 1 0 1 1 1 0 1 1 1 0 0 0 0 1
Given the set {1, 2, 3} match the relation on the left with the corresponding matrix on the right. {(1, 1), (1, 2), (1, 3)
1 1 1 0 0 0 0 0 0
Given the set {1, 2, 3} match the relation on the left with the corresponding matrix on the right. {(1, 1), (1, 2), (1, 3), (2, 2), (2, 3), (3, 3)}
1 1 1 0 1 1 0 0 1
(Select all that apply) Given the relation, {(1, 3), (2, 0), (2, 1), (2, 2), (3, 1), (3, 2), (3, 3)}, which of the following would be a valid path on it's directed graph?
1, 3, 3, 1, 3, 2, 0
Given the following table what will be the result of the SQL operation?
23, 23, 31, 31, 33
Match the ordered pairs on the left with the directed graphs on the right. {(a, a), (a, b), (b, a), (c, c), (c, b)}
A
Match the ordered pairs on the left with the directed graphs on the right. {(a, b), (b, c), (b, d), (c, a), (d, a), (d, c)}
B
The 3-tuples in a 3-ary relation represent the following of a product at a store: Barcode, Product Name, Product Brand. Which of these would likely be a primary key?
Barcode
Match the ordered pairs on the left with the directed graphs on the right. {(a, a), (a, b), (a, c), (b, a), (b, b), (b, c), (c, a), (c, b), (d, d)}
C
Match the ordered pairs on the left with the directed graphs on the right. {(a, a), (a, c), (b, a), (b, b), (b, c), (c, c)}
D
`Match the ordered pairs on the left with the directed graphs on the right. {(a, a), (a, b), (a, c), (b, a), (b, b), (b, c), (c, a), (c, b), (d, d)}
E
Match the ordered pairs on the left with the directed graphs on the right. {(a, a), (a, b), (b, a), (b, b), (c, a), (c, c), (c, d), (d,d)}
F
(Select all that apply) For the set, {2, 4, 6, 8} and the relation, {(2, 2), (4, 4), (6, 6)} determine whether this relation is reflexive, symmetric, antisymmetric, and transitive. (Could be multiple)
Transitive Symmetric Antisymmetric *In order for the relation to be reflexive it must at least contain an ordered pair (a, a) for every element of the set. Since it does not contain (8, 8) it is not reflexive. In order for the relation to be symmetric it must contain an ordered pair (b, a) for every ordered pair (a, b). We see that for every ordered pair (a, b) there is an ordered pair (b, a). (2, 2) and (2, 2) for instance. Therefore, it is symmetric. In order for the relation to be antisymmetric it must contain ordered pairs (b, a) and (a, b) such that b = a is implied. We see that for every ordered pair (a, b) there is an ordered pair (b, a) such that b = a is implied. Therefore, it is antisymmetric. In order for the relation to be transitive it must contain ordered pairs such that (a, b), (b, c), (a, c) are part of the relation. Since each is related to itself it must be transitive.
(Select all that apply) Which of the relations on {0, 1, 2, 3} are equivalence relations?
{(0, 0), (1, 1), (1, 2), (2, 1), (2, 2), (3, 3)} {(0, 0), (1, 1), (2, 2), (3, 3)}
Select all that apply) For the set, {1, 2, 3, 4} and the relation, {(1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4, 4)} determine whether this relation is reflexive, symmetric, antisymmetric, and transitive. (Could be multiple)
Transitive Symmetric Reflexive *In order for the relation to be reflexive it must at least contain an ordered pair (a, a) for every element of the set. Therefore, it must contain (1, 1), (2, 2), (3, 3), and (4, 4) in the relation and it does. In order for the relation to be symmetric it must contain an ordered pair (b, a) for every ordered pair (a, b). We see that (1, 2) and (2, 1) are in the relation thus it is symmetric. In order for the relation to be antisymmetric it must contain an ordered pair (b, a) such that b = a is implied. This is not the case since (1, 2) and (2, 1) are in the relation. In order for the relation to be transitive it must contain ordered pairs such that (a, b), (b, c), (a, c) are part of the relation. Since (1, 2) and (2, 1) are included and (1, 1) and (2, 2) are, too, then we can say the relation is transitive. (2, 1), (1, 2), (2, 2) (1, 2), (2, 1), (1, 1)
A non-empty directed graph in which all of the nodes have only one arc that points back to itself is an equivalent relation.
True
The 3-Tuples in a 3-ary relation represent the following attributes of a student database: student ID number, name, phone number. The student ID number will likely be the primary key.
True
(Select all that apply) Given the following directed graph which of the following are valid paths?
a, a, b, c, d, e, a b, c, d, e, a, a, a, a, b
What is the resulting ordered pair in the relation R from A={0, 1, 2, 3, 4} to B = {0, 1, 2, 3} where left parenthesis a comma space b right parenthesis thin space element of space R if and only if a = b?
{(0, 0), (1, 1), (2, 2), (3, 3)}\
What is the resulting ordered pair in the relation R from A={0, 2, 4, 6, 8} to B = {0, 1, 3, 5} where left parenthesis a comma space b right parenthesis thin space element of space R if and only if a > b?
{(2, 0), (2, 1), (4, 0), (4, 1), (4, 3), (6, 0), (6, 1), (6, 3), (6, 5), (8, 0), (8, 1), (8, 3), (8, 5)}
Given the relation R on the set {0, 1, 2, 3} containing the ordered pairs {(0, 1), (1, 1), (1, 2), (2, 0), (2, 2), (3, 0)} which of the following is the reflexive closure of R?
{(0, 0), (0, 1), (1, 1), (1, 2), (2, 0), (2, 2), (3, 0), (3, 3)} *The reflexive closure is will contain the original relation plus the additional ordered pairs of (1, 1), (2, 2), and (3, 3).
