5. Let A = {41, 49, 67, 71, 73, 76, 81, 88, 111} and R be an equivalence relation defined on A where aRb if and only if a = b mod 4. Show the partition of A defined by the equivalence classes of R. 2

Q: Let R be an equivalence relation on A = {a, b, c, d, e, f, g} such that aRc, cRd, dRg and bR f . If…

A: Given, R is an  equivalence relation onA={a, b, c, d, e, f, g}Such that  aRc, cRd, dRg, bRf

Q: 4. Let A = {a,b,c,d,e}. Suppose R is an equivalence relation on A. Suppose also that aRd and bRc,…

A: A=a,b,c,d,e R is an equivalence relation on A Also aRd and bRc, eRa and cRe

Q: (a) Give an example of a relation on the set {a, b, c, d] which is symmetric and transitive, but not…

A: (a) Given set is: a, b, c, d. To Do: We have to give an example of a relation on the given set a, b,…

Q: Let~ be the equivalence relation on Z defined by a ~ y if and only if x - y is divisible by 5. How…

A:

Q: 9.24. Let R be an equivalence relation on A = {a, b, c, d, e, f,g} such that a Rc, c Rd, d Rg and b…

A:

Q: 8. List the ordered pairs in the equivalence relations produced by these partitions of {a, b, c, d,…

A:

Q: Let S = {1;2;3;4}, and suppose that ~ is an equivalence relation on S: You are given the information…

A: Given: S=1, 2, 3, 4 and ~ is an equivalence relation on S. Also we have 1~2 and 2~3. To show: There…

Q: (a) How many elements are there in S/ ~ ? Equivalently, how man equivalence classes are there in S?…

A: This is a question of relation.

Q: 2. Suppose A = {1, 2, 3, 4, .. , 14, 15} and let R be the relation of congruence modulo 5 on the set…

A:

Q: 6. There are five different equivalence relations on the set A = {a,b,c}. Describe them all.…

A:

Q: For an integer n>4, let Sn be the set of all binary strings of length n. The relation R on Sn is…

A: Given,For an integer , let  be the set of all binary strings of length . The relation  on  is…

Q: 9.29. Let R be an equivalence relation defined on a set A containing the elements a, b, c and d.…

A:

Q: For a positive integer n ≥ 4, let {0, 1]" denote the set of all binary strings of length n. The…

A: For a positive integer n≥4, let 0,1n denote the set of all binary strings of length n. Observe that,…

Q: Show that each of the following relations equivalence classes. on Z is an equivalence relation, and…

A: In the given question we have to find the equivalence classes.

Q: 7. A relation R on a set X is called an equivalence relation if it is symmetric, reflexive, and…

A: Equivalence relation: A relation R on a set X is called an equivalence relation if it is symmetric,…

Q: The relation R on the set A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10) is defined by R= {(x,y) E AXA: xmod…

A:

Q: d) Determine whether Prove it, if not give Ris e) Determine whether If not Ris antisymmetric a…

A:

Q: 9. E is the binary relation defined on Z as follows: For all m, n E Z, m Enm-n is even. Is this an…

A: Equivalence relation

Q: Let R be the relation of congruence modulo 5. Which of the following equivalence classes are equal?…

A:

Q: 7. Let P be the congruence modulo 6 relation. Note, this is an equivalence relation. a. List 5…

A:

Q: Let R be a binary relation on A={1,2,3,43 defined a is related with b) if a²-b² is divisble by 3.…

A: Bartleby Guideline: According to Bartleby's guideline I can solve the first three subparts at a time…

Q: Indicate the partition of the set A={ x integer: 2 ≤ x ≤ 12 } resulting from the equivalence…

A:

Q: 8. Let A = {p, q, r, s, t, u, v}, and let R be the following equivalence relation on A: R = {(p, p),…

A: Equivalence Relation:            "A relation E on a set A is called an equivalence relation if E…

Q: Let R = {(a, b) | a = b (mod 3)} be an equivalence relation on the set of integers Z. What are the…

A:

Q: . Let S = P({1,2,3,4,5}.. Define equivalence class of the set {1,2,3}. equivalence relation ~ by X~Y…

A: Consider the given information:

Q: Consider the relation R = {(a,b) | a is congruent to b mod 3} on set A = {1, 2, 3, 4, 5, 6, 7, 8, 9,…

A: The equivalence classes are {1,4,7,10}, {2,5,8}, {3,6,9} Hence first option is correct

Q: Let S be the set of all binary strings. The relation R on S defined by aRb if a and b have the same…

A:

Q: Which of these relations on {0, 1, 2, 3} are equivalence relations? Determine the properties of an…

A:

Q: 14. For a,b E Z, define a ~ b if and only if 4a + b is a multiple of 5. Show that defines an…

A: