Question
In: Advanced Math
For each part below, find a binary relation on the set S = {1,2,3,4} that satisfies...
For each part below, find a binary relation on the set S = {1,2,3,4} that satisfies the given combination of properties
a) reflexive, symmetric, and transitive
b) not reflexive, but symmetric and transitive
c) not symmetric, but reflexive and transitive
d) not transitive, but reflexive and symmetric
e) neither reflexive nor symmetric, but transitive
f) neither reflexive nor transitive, but symmetric
g) neither symmetric not transitive, but reflexive
h) not reflexive, not symmetric, and not transitive
Solutions
Colby Messinger answered 3 years agoRelated Solutions
Let S = {1,2,3,4} and let A = SxS Define a relation R on A by...
Let S = {1,2,3,4} and let A = SxS
Define a relation R on A by (a,b)R(c,d) iff ad = bc
Write out each equivalence class (by "write out" I mean tell me
explicitly which elements of A are in each equivalence class)
Hint: |A| = 16 and there are 11 equivalence classes, so there
are several equivalence classes that consist of a single element of
A.
select the relation that is an equivalence relation. THe domain set is (1,2,3,4). a. (1,4)(4,1),(2,2)(3,3) b....
select the relation that is an equivalence relation. THe domain
set is (1,2,3,4).
a. (1,4)(4,1),(2,2)(3,3)
b. (1,4) (4,1)(1,3)(3,1)(2,2)
c. (1,4)(4,1)(1,1)(2,2)(3,3)(4,4)
d. (1,4)(4,1)(1,3)(3,1)(1,1)(2,2)(3,3)(4.4)
(6) In each part below, find a basis for R4 CONTAINED IN the given set, or...
(6) In each part below, find a basis for R4 CONTAINED IN the
given set, or explain why that is not possible: Do not use
dimension
(a) {(1,1,0,0),(1,0,1,0),(0,1,1,0)}
(b) {(1,−1,0,0),(1,0,−1,0),(0,1,−1,0),(0,0,0,1)}
(c) {(1,1,0,0),(1,−1,0,0),(0,1,−1,0),(0,0,1,−1)}
(d) {(1,1,1,1),(1,2,3,4),(1,4,9,16),(1,8,27,64),(1,16,81,256)}
(5) In each part below, find a basis for R4 that contains the given set, or...
(5) In each part below, find a basis for R4 that contains the
given set, or explain why that is not possible: (a)
{(1,1,0,0),(1,0,1,0),(0,1,1,0)} (b)
{(1,−1,0,0),(1,0,−1,0),(0,1,−1,0)} (c)
{(1,1,0,0),(1,−1,0,0),(0,1,−1,0),(0,0,1,−1)} (d)
{(1,1,1,1),(1,2,3,4),(1,4,9,16),(1,8,27,64),(1,16,81,256)}
Show that the given relation R is an equivalence relation on set S. Then describe the...
Show that the given relation R is an equivalence relation on set
S. Then describe the equivalence class containing the given element
z in S, and determine the number of distinct equivalence classes of
R.
Let S be the set of all possible strings of 3 or 4 letters, let
z = ABCD and define x R y to mean that x has the same first letter
as y and also the same third letter as y.
Set A = {1, 2, 3, 4}, write a binary relation R on A that is...
Set A = {1, 2, 3, 4}, write a binary relation R on A that is
reflexive, symmetric and transitive, with (1, 2),(3, 2) ∈ R.
Find a recurrence relation for the number of binary strings of length n which do not...
Find a recurrence relation for the number of binary strings of
length n which do not contain the substring 010
(1) In each part, decide whether or not the described relation is an equivalence relation. Explain...
(1) In each part, decide whether or not the described relation
is an equivalence relation.
Explain your answers.
(a)
A
is the set of all residents of the United States. The
relation
∼
on
A
given by:
x
∼
y
if
x, y
are in the same state at noon on November 3rd.
(b)
U
is the set of all undergraduates at the University of Oregon.
The relation
∼
on
U
given by:
x
∼
y
if
x, y
are...
1)Let S be the set of all students at a college. Define a relation on the...
1)Let S be the set of all students at a college. Define a
relation on the set S by the rule that two people are related if
they live less than 2 miles apart. Is this relation an equivalence
relation on S? Justify your answer.
2) Define another relation on the set S from problem 5 by
defining two people as related if they have the same classification
(freshman, sophomore, junior, senior or graduate student). Is this
an equivalence relation...
1)Let S be the set of all students at a college. Define a relation on the...
1)Let S be the set of all students at a college. Define a
relation on the set S by the rule that two people are related if
they live less than 2 miles apart. Is this relation an equivalence
relation on S? Justify your answer.
2) Define another relation on the set S from problem 5 by
defining two people as related if they have the same classification
(freshman, sophomore, junior, senior or graduate student). Is this
an equivalence relation...
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