- Let and x be relations on Z defined as follows: For a, be Z, a~b if and only if 2 divides a +b. • For a, b e Z, az b if and only if 3 divides a +b. (a) Is ~ an equivalence relation on Z2 If not, is this relation reflexive, symmetric, or transitive? (b) Is an equivalence relation on Z2 If not, is this relation reflexive, symmetric, or transitive?
- Let and x be relations on Z defined as follows: For a, be Z, a~b if and only if 2 divides a +b. • For a, b e Z, az b if and only if 3 divides a +b. (a) Is ~ an equivalence relation on Z2 If not, is this relation reflexive, symmetric, or transitive? (b) Is an equivalence relation on Z2 If not, is this relation reflexive, symmetric, or transitive?
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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Transcribed Image Text:(b) Use set builder notation (without using the symbol ~) to specify the set
C.
(c) Use the roster method to specify the set C.
10. Let and be relations on Z defined as follows:
• For a, be Z, a~b if and only if 2 divides a + b.
• For a, be Z, a b if and only if 3 divides a + b.
(a) Is an equivalence relation on Z? If not, is this relation reflexive,
symmetric, or transitive?
(b) Is an equivalence relation on Z? If not, is this relation reflexive,
symmetric, or transitive?
11. Let U be a finite, nonempty set and let P(U) be the power set of U. That
is, P(U) is the set of all subsets of U. Define the relation ~ on P(U) as
follows: For A, B E P(U), A ~ B if and only if ANB= 0. That is, the
ordered pair (A, B) is in the relation if and only if A and B are disjoint.
Is the relation ~ an equivalence relation on P(U)? If not, is it reflexive,
symmetric, or transitive? Justify all conclusions
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