Deck 9: A: Relations

Question 1

determine whether the binary relation is:
(1) reflexive, (2) symmetric, (3) antisymmetric, (4) transitive.
The relation R on the set of all subsets of {1, 2, 3, 4} where SR T means

Answer 1

1, 4

Question 2

determine whether the binary relation is:
(1) reflexive, (2) symmetric, (3) antisymmetric, (4) transitive.
The relation R on the set of all people where aR b means that a is younger than b.

Answer 2

1, 2

Question 3

determine whether the binary relation is:
(1) reflexive, (2) symmetric, (3) antisymmetric, (4) transitive.
The relation R on Z where aR b means

Answer 3

1, 2

Question 4

determine whether the binary relation is:
(1) reflexive, (2) symmetric, (3) antisymmetric, (4) transitive.
The relation R on Z where aR b means

Question 5

determine whether the binary relation is:
(1) reflexive, (2) symmetric, (3) antisymmetric, (4) transitive.
The relation R on A = {x, y, z} where R = {(x, x), (y, z), (z, y)}.

Question 6

List the reflexive relations on the set {0, 1}.

Question 7

determine whether the binary relation is:
(1) reflexive, (2) symmetric, (3) antisymmetric, (4) transitive.
The relation R on the set of all people where aR b means that a is at least as tall as b.

Question 8

List the transitive relations on the set {0, 1}.

Question 9

determine whether the binary relation is:
(1) reflexive, (2) symmetric, (3) antisymmetric, (4) transitive.

Question 10

List the asymmetric relations on the set {0, 1}.

Question 11

determine whether the binary relation is:
(1) reflexive, (2) symmetric, (3) antisymmetric, (4) transitive.

Question 12

List all the binary relations on the set {0, 1}.

Question 13

List the symmetric relations on the set {0, 1}.

Question 14

determine whether the binary relation is:
(1) reflexive, (2) symmetric, (3) antisymmetric, (4) transitive.
The relation R on Z where aR b means

Question 15

determine whether the binary relation is:
(1) reflexive, (2) symmetric, (3) antisymmetric, (4) transitive.
The relation R on {w, x, y, z} where R = {(w, w), (w, x), (x, w), (x, x), (x, z), (y, y), (z, y), (z, z)}.

Question 16

List the relations on the set {0, 1} that are reflexive and symmetric.

Question 17

List the irreflexive relations on the set {0, 1}.

Question 18

List the antisymmetric relations on the set {0, 1}.

Question 19

List the relations on the set {0, 1} that are neither reflexive nor irreflexive.

Question 20

determine whether the binary relation is:
(1) reflexive, (2) symmetric, (3) antisymmetric, (4) transitive.
The relation R on {1, 2, 3, . . .} where aR b means a | b.

Question 21

supp ose R and S are relations on {a, b, c, d}, where
Find the combination of relations.

Question 22

supp ose R and S are relations on {a, b, c, d}, where
Find the combination of relations.

Question 23

suppose that the transactions at a fast-food restaurant during one afternoon are {hamburger,
fries, regular soda}, {cheeseburger, fries, regular soda}, {apple, hamburger, fries, regular soda}, {salad, diet
soda}, {hamburger, onion rings, regular soda}, {cheeseburger, fries, onion rings, regular soda}, {hamburger, fries},
{hamburger, fries, regular soda}.
Find the count and support of {cheeseburger}.

Question 24

find the matrix that represents the given relation. Use elements in the order given to determine
rows and columns of the matrix.

Question 25

find the matrix that represents the given relation. Use elements in the order given to determine
rows and columns of the matrix.

Question 26

supp ose R and S are relations on {a, b, c, d}, where
Find the combination of relations.

Question 27

find the matrix that represents the given relation. Use elements in the order given to determine
rows and columns of the matrix.

Question 28

find the matrix that represents the given relation. Use elements in the order given to determine
rows and columns of the matrix.

Question 29

find the matrix that represents the given relation. Use elements in the order given to determine
rows and columns of the matrix.

Question 30

find the matrix that represents the given relation. Use elements in the order given to determine
rows and columns of the matrix.

Question 31

determine whether the binary relation is:
(1) reflexive, (2) symmetric, (3) antisymmetric, (4) transitive.

Question 32

determine whether the binary relation is:
(1) reflexive, (2) symmetric, (3) antisymmetric, (4) transitive.

Question 33

A company makes four kinds of products. Each product has a size code, a weight code, and a shape code. The following table shows these codes: Find which of the three codes is a primary key. If none of the three codes is a primary key, explain why.

Question 34

supp ose R and S are relations on {a, b, c, d}, where
Find the combination of relations.

Question 35

supp ose R and S are relations on {a, b, c, d}, where
Find the combination of relations.

Question 36

find the matrix that represents the given relation. Use elements in the order given to determine
rows and columns of the matrix.

Question 37

suppose that the transactions at a fast-food restaurant during one afternoon are {hamburger,
fries, regular soda}, {cheeseburger, fries, regular soda}, {apple, hamburger, fries, regular soda}, {salad, diet
soda}, {hamburger, onion rings, regular soda}, {cheeseburger, fries, onion rings, regular soda}, {hamburger, fries},
{hamburger, fries, regular soda}.
Find all frequent itemsets if the threshold level is 0.6.

Question 38

find the matrix that represents the given relation. Use elements in the order given to determine
rows and columns of the matrix.

Question 39

If X=( Fran Williams, 617885197, MTH 202, 248B West ) , find the projections

Question 40

supp ose R and S are relations on {a, b, c, d}, where
Find the combination of relations.

Question 41

If R = {(1, 2), (1, 4), (2, 3), (3, 1), (4, 2)}, find the symmetric closure of R.

Question 42

Let
Determine if R is: (a) reflexive, (b) symmetric, (c) antisymmetric, (d) transitive.

Question 43

Let https://d2lvgg3v3hfg70.cloudfront.net/TB34225555/.
Determine if R is: (a) reflexive, (b) symmetric, (c) antisymmetric, (d) transitive.

Question 44

The diagram at the right is the Hasse diagram for a partially ordered set. Referring to this diagram:

Question 45

Draw the directed graph for the relation defined by the matrix

Question 46

Question 47

find the matrix that represents the given relation. Use elements in the order given to determine
rows and columns of the matrix.

Question 48

Find the join of the 3-ary relation {(Wages, MS410, N507), (Rosen, CS540, N525), (Michaels, CS518, N504), (Michaels, MS410, N510)} and the 4-ary relation {(MS410, N507, Monday, 6:00), (MS410, N507, Wednesday, 6:00), (CS540, N525, Monday, 7:30), (CS518, N504, Tuesday, 6:00), (CS518, N504, Thursday, 6:00)} with respect to the last two fields of the first relation and the first two fields of the second relation.

Question 49

Find the transitive closure of if is

Question 50

find the matrix that represents the given relation. Use elements in the order given to determine
rows and columns of the matrix.

Question 51

Draw the directed graph for the relation defind by the matrix

Question 52

Find the smallest partial order relation on {1, 2, 3} that contains (1, 1), (3, 2), (1, 3).

Question 53

Find the smallest equivalence relation on {1, 2, 3} that contains (1, 2) and (2, 3).

Question 54

Which of the following are partitions of {1, 2, 3, . . . , 10}? (a) {2, 4, 6, 8}, {1, 3, 5, 9}, {7, 10} (b) {1, 2, 4, 8}, {2, 5, 7, 10}, {3, 6, 9} (c) {3, 8, 10}, {1, 2, 5, 9}, {4, 7, 8} (d) {1}, {2}, . . . , {10} (e) {1, 2, . . . , 10}

Question 55

What is the covering relation of the partial ordering on the set {2,4,6,8,10,12} ?

Question 56

If R = {(1, 2), (1, 4), (2, 3), (3, 1), (4, 2)}, find the reflexive closure of R.

Question 57

What is the covering relation of the partial ordering on the set {1,2,3,4,6,8,12,24} ?

Question 58

Suppose A = {2, 3, 6, 9, 10, 12, 14, 18, 20} and R is the partial order relation defined on A where xR y means

Question 59

If R = {(x, y) | x and y are bit strings containing the same number of 0s}, find the equivalence classes of (a) 1 (b) 00 (c) 101

Question 60

Draw the Hasse diagram for the relation

Question 61

Suppose |A| = n. Find the number of symmetric binary relations on A.

Question 62

Let R be the relation on A = {1, 2, 3, 4, 5} where R = {(1, 1), (1, 3), (1, 4), (2, 2), (3, 1), (3, 3), (3, 4), (4, 1), (4, 3), (4, 4), (5, 5)}. R is an equivalence relation. Find the equivalence classes for the partition of A given by R.

Question 63

Suppose A is the set composed of all ordered pairs of positive integers. Let R be the relation defined on A where (a,
b)R(c,
d) means that a + d = b + c.
(a) Prove that R is an equivalence relation.
(b) Find [(2, 4)].

Question 64

Suppose |A| = n. Find the number of reflexive, symmetric binary relations on A.

Question 65

Suppose the relation R is defined on the set Z where aR b means that ab ≤ 0. Determine whether R is an equivalence relation on Z .

Question 66

Let R be the relation on A = {1, 2, 3, 4, 5} where R = {(1, 1), (1, 3), (1, 4), (2, 2), (3, 1), (3, 3), (3, 4), (4, 1), (4, 3), (4, 4), (5, 5)}. Draw the directed graph for R.

Question 67

give an example or else prove that there are none.
A relation on {1, 2, 3} that is reflexive and transitive, but not symmetric.

Question 68

Suppose that R and S are equivalence relations on a set A. Prove that the relation R ∩ S is also an equivalence relation on A.

Question 69

give an example or else prove that there are none.
A relation on {a, b, c} that is reflexive and transitive, but not antisymmetric.

Question 70

Let R be the relation on A = {1, 2, 3, 4, 5} where R = {(1, 1), (1, 3), (1, 4), (2, 2), (3, 1), (3, 3), (3, 4), (4, 1), (4, 3), (4, 4), (5, 5)}. Write the matrix for R.

Question 71

Suppose |A| = n. Find the number of binary relations on A.

Question 72

give an example or else prove that there are none.
A relation on {1, 2} that is symmetric and transitive, but not reflexive.