(i) The equivalence class [b] determined by b E B is a non-empty set. 1 (ii) If r and y are elements of B such that rRy, then [r] = [y]. (iii) The distinct equivalence classes of S form a partition of B. (iv) S is a partial order relation. (v) If z and y are elements of B such that r + y and rSy, then (y,1) ¢ S.
(i) The equivalence class [b] determined by b E B is a non-empty set. 1 (ii) If r and y are elements of B such that rRy, then [r] = [y]. (iii) The distinct equivalence classes of S form a partition of B. (iv) S is a partial order relation. (v) If z and y are elements of B such that r + y and rSy, then (y,1) ¢ S.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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can i get some help with binary and relation true or false question
Let S and T be equivalence relations on a set B.
![(i) The equivalence class [b] determined by b E B is a non-empty
set.
1
(ii) If r and y are elements of B such that xRy, then [r] = [y].
(iii) The distinct equivalence classes of S form a partition of B.
(iv) S is a partial order relation.
(v) If x and y are elements of B such that r + y and rSy, then
(y, x) 4 S.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9345e68a-07d5-4873-bd1a-34b401327ec2%2F6af1b33f-d475-4a79-ad63-0e61e4de950c%2Ffq05iyq_processed.png&w=3840&q=75)
Transcribed Image Text:(i) The equivalence class [b] determined by b E B is a non-empty
set.
1
(ii) If r and y are elements of B such that xRy, then [r] = [y].
(iii) The distinct equivalence classes of S form a partition of B.
(iv) S is a partial order relation.
(v) If x and y are elements of B such that r + y and rSy, then
(y, x) 4 S.
Expert Solution
Step 1
Given that S and T are equivalence relation on a set B.
i ) the equivalence class [b] determined by b in B is a non empty set. ~ True , since b itself belong to the set B.
ii) If x and y are two elements in B and xRy ,then [x] = [y].
~ True.
iii)The distinct equivalence classes of S forms a partition of B.
~ True.
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