Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
Bartleby Related Questions Icon

Related questions

Q: 6. Let S be a set and suppose is a relation on S. For each of the following, provide a…
A: Let us solve the given problems on relation in the next steps.
Q: In Q1-Q4 prove why each relation has or does not have the properties: reflexive, symmetric,…
A: Since you have asked  multiple questions so as per guidelines we will solve  the first question for…
Q: ~ Define an equivalence relation on Z by a b if a - b is even. Show that . equivalence relation.…
A:
Q: uts) Do the following for the set X = {1,2,3,4,5). 7. (a) Give an example of a relation on X that is…
A:
Q: Define a relation on R by a ~ b iff aª – b² = bª – a². (a) Show that ~ is an equivalence relation.…
A: (a). To show that the given relation is an equivalence relation, we need to show that it is…
Q: 6. A relation R on a set X is called a total order if it is antisymmetric, reflexive, transi- tive,…
A:
Q: We have defined the relations ≡6 and ≡10 to be certain subsets of Z^2 . Their intersection R =…
A:
Q: We defined the relation between sets by A ~ B means that there there is a 1-1 correspondence ƒ : A →…
A: We define the relation ~ between sets by A~B means that there is a one-one correspondence f:A→B Show…
Q: on P(X), where X = Y, Z E P(X), we say Y - Z if and only if Y has the same number of ele- Define a…
A: Given a set X={1,2,3,4,5,6}. Define a relation ~ on P(X) as : For Y,Z∈ P(X), we say  Y~Z if and only…
Q: 3. Show that the relation R (called lexicographic ordering) defined on Z x Z by: (a, b)R(c, d) if (a…
A: The lexicographic ordering relation R on ℤ×ℤ is defined by, a, bRc, d if a>c or a=c and b≥d Show…
Q: 9. Define a relation R on {-2,-1,0, 1, 2, 3, 4, 5, 6, 7} by a R b if and only if 3a+b is a multiple…
A:
Q: Decide whether each of the following relations is an equivalence relation or not.  {(a, b) | gpa of…
A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…
Q: Let A be a set and R = {(x, x) : x ∈ A} be the is-equal-to relation on A. Prove that a relation S on…
A: We are given any non-empty set A, on which a relation R = { (x, x) : x∈A } is defined.  Let S be any…
Q: In each of the following cases of a set X and relation determine whether ~ is reflexive, symmetric,…
A: “Since you have posted multiple questions, we will provide the solution only to the first question…
Q: Exercise 1.2. Determine whether the following relations ~ is an equivalence relation: (1) nm in Z if…
A: Step 1:Step 2:Step 3: Step 4:
Q: 1. Suppose A = {1,2, 3, 4} and the relation R on A is R = {(1,1), (2, 2), (3,3), (3, 4), (4, 4)} (a)…
A:
Q: Give an example of an equivalence relation R on the set Q such that there are exactly three distinct…
A: We take the help of the signum function
Q: Which of the following is an equevalence relation on the set (a, b, c} 7 O (a, a), (a, b), (b, a).…
A: Option 1 is equivalence relation. Option 2 is also is an equivalence relation. Option 3 and 4 is not…
Q: (Chapter 11.4, #3) The relation relation. Sketch it, by drawing Z as a subset of the line, then…
A: The objective is to show that x≡ymod4 is an equivalence relation. To show the relation is an…
Q: 5. Let X be the set X = {1,2,3}, and let R be the relation defined on X by x₁ Rx₂ if x1 + x2 3. (a)…
A:
Q: Let A # 0 be a set. Prove that A? is an equivalence relation on A.
A:
Q: (a) Show that the relation defined on Z by m~n if 4m +n is divisible by 5 2 is an equivalence…
A:
Q: A relation on a set A is circular iff , y, z x~y and y~z implies z~x. Prove that a relation is an…
A: The relation on a set is a subset of the Cartesian product of the set. Therefore, each element is in…
Q: 7. Let A = {1,2,3,4}x{1,2,3,4}. Define an equivalence relation ~ by (x1,x2) ~ (x3,xa) iff xxx2 =…
A: Let A=1,2,3,4×1,2,3,4. The equivalence relation ~  is defined by,        "x1,x2~x3,x4 only if…
Question
7. A relation \( R \) on a set \( X \) is called an equivalence relation if it is symmetric, reflexive, and transitive. (a) Show that congruence modulo \( m \) (the relation on \( \mathbb{Z} \) where we write \( x \equiv_m y \) if \( m|(x-y) \)) is an equivalence relation. (b) Show that every partition \( P \) of a set \( X \) defines an equivalence relation \( \sim \) by declaring \( x \sim y \) if \( x \) and \( y \) are in the same partition element.
expand button
Transcribed Image Text:7. A relation \( R \) on a set \( X \) is called an equivalence relation if it is symmetric, reflexive, and transitive. (a) Show that congruence modulo \( m \) (the relation on \( \mathbb{Z} \) where we write \( x \equiv_m y \) if \( m|(x-y) \)) is an equivalence relation. (b) Show that every partition \( P \) of a set \( X \) defines an equivalence relation \( \sim \) by declaring \( x \sim y \) if \( x \) and \( y \) are in the same partition element.
Expert Solution
Check Mark
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
See solutionCheck out a sample Q&A here
Step 1: Basic information
VIEW
Step 2: To prove 7(a) ,7(b)
VIEW
Solution
VIEW
bartleby

Step by stepSolved in 3 steps with 2 images

See solution
Check out a sample Q&A here
Blurred answer
Knowledge Booster
Background pattern image
Similar questions
Recommended textbooks for you
Text book image
Advanced Engineering Mathematics
Advanced Math
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Wiley, John & Sons, Incorporated
Text book image
Numerical Methods for Engineers
Advanced Math
ISBN:9780073397924
Author:Steven C. Chapra Dr., Raymond P. Canale
Publisher:McGraw-Hill Education
Text book image
Introductory Mathematics for Engineering Applicat...
Advanced Math
ISBN:9781118141809
Author:Nathan Klingbeil
Publisher:WILEY
Text book image
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
Text book image
Basic Technical Mathematics
Advanced Math
ISBN:9780134437705
Author:Washington
Publisher:PEARSON
Text book image
Topology
Advanced Math
ISBN:9780134689517
Author:Munkres, James R.
Publisher:Pearson,
SEE MORE TEXTBOOKS