Consider the family of sets S - [{1,5, 6), (2,4,6), (4,5, 6), (2,5, 6), (3,4, 5}, {1,4, 6}). (1.1) and let Y - (1,3,4,5). Define the relation Ron S by (A, B) eR AY=B\Y, where A, B are arbitrary elements of S. 0 (a) Since for every A ES A\Y-\Y, where the relation R (here and below in (b-d), please type is or is not in the input field below) is reflexive. (b) Given any A, BES, we have that A\Y-B\YB\Y-L\Y where 2 - A and hence the relation R is symmetric. (e) For every A, B,Ce s, (A\Y = B\Y) and (B\Y =C\Y) mplies A\Y -L\Y, where and hence the relation R is transitive. (d) Accordingly, by (a,bc), the relation R is an equivalence relation on S. (1) Find the matrix Mg of the relation FR (please enter the matrix row-by-row in the six input fields below, when entering each row, separate the entries by single spaces; understandably, the i-th row/column of the matrix Mg must correspond to the f-th set A, in the list of the elements of S given in Eg (1.1) above): (H) if your answer in (d) in part (0) is yes, describe the equivalence classes by the relation R below (please enter the sets A, in each equivalence class so that their indices are in increasing order, similar to A- (A1,4. 3, A 5 ) } [44] - { [Aal = { [A3] = { [A -{ [As) - ( [Aal - {
Consider the family of sets S - [{1,5, 6), (2,4,6), (4,5, 6), (2,5, 6), (3,4, 5}, {1,4, 6}). (1.1) and let Y - (1,3,4,5). Define the relation Ron S by (A, B) eR AY=B\Y, where A, B are arbitrary elements of S. 0 (a) Since for every A ES A\Y-\Y, where the relation R (here and below in (b-d), please type is or is not in the input field below) is reflexive. (b) Given any A, BES, we have that A\Y-B\YB\Y-L\Y where 2 - A and hence the relation R is symmetric. (e) For every A, B,Ce s, (A\Y = B\Y) and (B\Y =C\Y) mplies A\Y -L\Y, where and hence the relation R is transitive. (d) Accordingly, by (a,bc), the relation R is an equivalence relation on S. (1) Find the matrix Mg of the relation FR (please enter the matrix row-by-row in the six input fields below, when entering each row, separate the entries by single spaces; understandably, the i-th row/column of the matrix Mg must correspond to the f-th set A, in the list of the elements of S given in Eg (1.1) above): (H) if your answer in (d) in part (0) is yes, describe the equivalence classes by the relation R below (please enter the sets A, in each equivalence class so that their indices are in increasing order, similar to A- (A1,4. 3, A 5 ) } [44] - { [Aal = { [A3] = { [A -{ [As) - ( [Aal - {
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Consider the family of sets
S= [{1,5, 6}, {2,4, 6), (4, 5, 6), {2, 5, 6}, {3,4, 5}, {1, 4, 6}].
(1.1)
and let
Y - (1,3, 4, 5}.
Define the relation Ron S by
(A, B) ER = A\Y = B\Y,
where A, B are arbitrary elements of S.
(1) (a) Since for every A ES
A\Y = \Y,
where
? = B
,the relation R (here and below in (b-d), please type is or is not in the input field below)
is
reflexive.
(b) Given any A, BES, we have that
A\Y = B\Y = B\Y= \Y
where
and hence the relation R
is
symmetric.
(c) For every A, B, CES,
(A\Y = B\Y) and (B\Y = C\Y)
implies
A\Y = \Y,
where
al=
,and hence the relation R
is
transitive.
(d) Accordingly, by (a,b,c), the relation R
is
an equivalence relation on S.
(11) Find the matrix MR of the relation R (please enter the matrix row-by-row in the six input fields below, when entering each row, seperate the entries by single spaces;
understandably, the i-th row/column of the matrix MR must correspond to the i-th set A, in the list of the elements of S given in Eq. (1.1) above):
(I) If your answer in (d) in part () is yes', describe the equivalence classes by the relation R below (please enter the sets A, in each equivalence class so that their
indices are in increasing order, similar to
Ag = {A 1, A 3, A 5| }
):
[44] = {
[Ag] = {
[43] = {
[A4] - {
}
[A4] = {
[Ag] = {
}
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbee2d141-5e4b-4e88-bda3-55b2c14c938b%2Fd50cd3b3-b2a3-4cbe-a6a2-cd1533bb387e%2Fjw67yl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the family of sets
S= [{1,5, 6}, {2,4, 6), (4, 5, 6), {2, 5, 6}, {3,4, 5}, {1, 4, 6}].
(1.1)
and let
Y - (1,3, 4, 5}.
Define the relation Ron S by
(A, B) ER = A\Y = B\Y,
where A, B are arbitrary elements of S.
(1) (a) Since for every A ES
A\Y = \Y,
where
? = B
,the relation R (here and below in (b-d), please type is or is not in the input field below)
is
reflexive.
(b) Given any A, BES, we have that
A\Y = B\Y = B\Y= \Y
where
and hence the relation R
is
symmetric.
(c) For every A, B, CES,
(A\Y = B\Y) and (B\Y = C\Y)
implies
A\Y = \Y,
where
al=
,and hence the relation R
is
transitive.
(d) Accordingly, by (a,b,c), the relation R
is
an equivalence relation on S.
(11) Find the matrix MR of the relation R (please enter the matrix row-by-row in the six input fields below, when entering each row, seperate the entries by single spaces;
understandably, the i-th row/column of the matrix MR must correspond to the i-th set A, in the list of the elements of S given in Eq. (1.1) above):
(I) If your answer in (d) in part () is yes', describe the equivalence classes by the relation R below (please enter the sets A, in each equivalence class so that their
indices are in increasing order, similar to
Ag = {A 1, A 3, A 5| }
):
[44] = {
[Ag] = {
[43] = {
[A4] - {
}
[A4] = {
[Ag] = {
}
%3D
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