1. Let m € Z'. Show that = 721 is an equivalence relation on Z.

Q: QUESTION 7 Given binary relation, R = {(0, 0),(1, 1),(2,2) } is is defined on set on A = {0, 1, 2,…

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Q: Part 2. Each relation given below is a partial order. Draw the Ilasse diagram for he partial order.

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Q: R, S, and T are relations defined on A {0, 1, 2, 3}. Let S = {(0, 0), (0, 3), (1, 0), (1, 2), (2,…

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Q: Consider the four following relations on A = {1,2, 3}: R = {(1, 1), (1,3), (2, 2), (3, 1)}, R2 =…

A: Relation

Q: Identify the relation on set (1,2,3,4} if it is reflexive, symmetric, antisymmetric or transitive.…

A: We know that , relation is relationship between sets of values. A binary relation R defined on set A…

Q: 7 Part 3 of 4 ! Required information NOTE: This is a multi-part question. Once an answer is…

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Q: R relation for A = {a, b, c, d, e, f} partially ordered set and subset B = {b, c, d} Let R = {(b,…

A: Given data: R=b,a,c,d,d,b,e,c,f,d,e,d,f,c which is relation for A=a,b,c,d,e,f partially ordered set…

Q: The relation…

A: Given: R is a relation from A to A such that A=1,2,3,4,5 &…

Q: write answer as fraction -(1/2)^3

A: We know , (a/b)n = an/bn

Q: Let R be the relation defined by x R y =x<y° Determine if R is an order relation on N? on Z? Justify…

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Q: operational sets

A: It is given that, the set is

Q: Each matrix below represents a relation. The rows and columns are numbered 1 through 3 or 4. Give…

A: We have to find the Arrow diagram and relation as a set of ordered pairs for the Matrices in part a.…

Q: Question Show. is Banach space

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Q: Let A={1,5,6,8,10} and R={(1,1), (5,5), (8,8), (10,10),

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Q: 17. Equivalence relations 1. Let X = {a, b, c, d, e, f} and R be the relation on X defined by R =…

A: The given relation is an equivalence relation. The equivalence classes are given below.

Q: Let R be a relation over set A. Let A = {1,2, 3, 4, 5, 6} and let R = {(a, b) e A² : |a – b| > 3} a)…

A: A relation R on a set A which is a subset of  A×A is said to be reflexive if for any x∈A,x,x∈R.  A…

Q: a set A = {1,2, 3, 4} of numbers and a set B = {a, b, c, d} of letters. {(1, d), (2, d) , (3, a) ,…

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Q: What is Partial Ordering Relation and give an example.   What is Equivalence Relation and give an…

A: See the attachment

Q: |Given the relation R= {(1,1), (2, 4), (3, 1), (4, 1), (5,2)} on the set A= {1,2,3,4,5), find the…

A: We know: Symmetric closure of a relation R, △, is obtained by adding (b, a) to R for each (a, b) ∈ R…

Q: Relations Given the sets over the domain {a, b, c, d}: A = { (a, a), (b, b), (d, d), (b, a) } B = {…

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Q: 3. Show that the relation R (called lexicographic ordering) defined on Z x Z by: (a, b)R(c, d) if (a…

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Q: Let A {1,3,5, ... }, then A is well- ordered.

A: Here we have given a set A ={1,3,5,  ...}

Q: QUESTION 6. L Consider the following relation R on the set A = {1,2,3,4,5} R = {(1, 1), (2, 2),…

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Q: Question 2 How many relations are there on the set A in Question 1? Give the reasoning for your…

A: As we know from the definition of relation on a set that every relation on a set is an element of…

Q: a) For the relation R on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it is an…

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Q: 5. If X any Y are sets, then X-Y= {r€ X: 1¢Y} If X is open set and Y is closed set. Prove that (a)…

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Q: (b) The domain is fa, b, e, d, e, f). The relation is the set: (b, e), (b, d). (c, a), (c. S). (a,…

A: Given: The relation of a set a, b, c, d, e, f is b, e, b, d, c, a, c, f, a, f, a, a, b, b, c, c, d,…

Q: (d) Let x be the complex number 1-i. Use de Moivre's Theorem to find the smallest n E N such that x"…

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Q: 8 11 Part 4 of 4 Required information NOTE: This is a multi-part question. Once an answer is…

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Q: Suppose denotes an equivalence relation on a set A and a, b E A. Then a b if and only if anb=0.

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Q: Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be…

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Q: Let A = {1, 2, 3, 4). Define a relation R on A: R = {(1, 2), (1, 3), (2, 2), (2, 3), (3, 4), (4,3)}…

A: Since you have posted a multi subparts question according to guidelines I will solve first…

Q: Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be…

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Q: The following is an arrow diagram for the relation on the set {1, 2, 3, 4). 1 3 2 4 Match the…

A: In the arrow diagram of a relation, if the arrow is pointing from A to B, then it can be represented…

Q: what is the dominating sets ? And give examples

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Q: Let A = {2,7,8,10} and B = {1,5,8,12} and let & be the "greater than or equal to" relation. That is,…

A: The given sets are A=2,7,8,10 and B=1,5,8,12 To find: The ordered pairs which satisfies σ and σ-1

Q: b. Which sets are functions?• (1, 2) (2, 3) (3, 4) Yes/No If no, why• (1, 2), (2, 3) (2, 5) Yes/No…

A: We have given,

Q: a. Write a set of ordered pairs that defines the relation. b. State the domain of the relation. c.…

A: Given table : Instrument Bass Drums Guitar Guitar Player John Mark Bob Petty

Q: what is an independent dominating set ? And give examples

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