Question (1) (i) Define Relation .                               (ii) Difference between Union and Intersection of sets with one example

Q: Questio The relation R = {(1, 1), (1, 2), (3, 2), (2, 4)} on the set A = {1, 2, 3, 4} is an…

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Q: 7. Which of these relations on the set of all people are equivalence relation? a) {(x, y)\x and y…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: 7. (Relations) Consider the set A = (1,2,3, 4, 5}, and a relation R defined by zRy + 2-y is an…

A: Note: Our guidelines we are supposed to answer only three subpart . Kindly repost other subpart as…

Q: (b) Define Equivalence Relation with an example. Give an example of a relation which is not…

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Q: (1,1),(2,2),(3,3)(4,4),(5,5) relation or function?

A: Given: R=(1, 1), (2, 2), (3, 3), (4, 4), (5, 5) To determine: Given set is a relation or function.

Q: Show that compact sets are closed under arbitrary intersections and finite unions. (Here we're…

A: To show that compact sets are closed under arbitrary intersections and finite unions

Q: If a set is empty then number of subsets

A: Given : Empty set :   It is the unique set which does not contain any element is called as empty set…

Q: 1. List the domain and range for the relation. {(11, -5), (-10, 15), (3, 5), (7,-5)} O Range: {-5,7,…

A: Domain is the values of x and range is the values of y in ordered pairs ( x , y )

Q: Solve the problem by combinatorics. Let X be an n-element set. Prove that there are 3^n ordered…

A: Let X be an n-element set. Prove that there are 3^n  ordered pairs (A,B) of subsets of X such that…

Q: operational sets

A: It is given that, the set is

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: )Determine the power set of the set A={q,p,x}. 2)Let the relation R be {(1,2), (2,9), (5,6)}. Is R…

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Q: True or False?  Every infinite set is unbounded.

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Q: Limikadity malfing ASomozphic Oxdexed sets:-

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Q: Part A: Suppose R is a relation defined on the set A = {1,2,3}. If R =…

A: Reflexive Property The Reflexive Property states that for every real number x , x=x . Symmetric…

Q: 7. (Relations) Consider the set A= (1,2, 3, 4, 5), and a relation R defined by zRy -y is an integor…

A: Given, A = 1, 2, 3, 4, 5xRy ⇔x2-y is an integer multiple of 3.

Q: an equivalence relation c

A: (a) Given, the function                                      id : X→ X     defined by…

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

A: See the attachment

Q: A relation is an equivalence relation if it satisfies three properties. which of the following…

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: Example 1.2.1 Here are two simple examples of set equality on the real line for you to verify. ) U0,…

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Q: Bounded Julia (ExH). Why is no Julia Set unbounded?

A: 37)

Q: Using Richard Hammack's book of Elements of Discrete Mathematics chapter 18 in cardinality. Prove…

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Q: True or False: A Partial Order Relation is transitive, symmetric, and reflexive. True False

A: A partial order Relation is transitive, antisymmetric and reflexive.

Q: QUESTION 3 If A = {2, 3, 4, 5} and R is a relation on A such that x R y if R = {(x, y) : (x + y) is…

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Q: EXAMPLE 1 Expressing Sets in Interval Notation and Set-Builder Notation Complete the table. Interval…

A: Given:              From the giver graph Interval Notation: (-∞, 5]

Q: Proficiency #18. [Equivalence Relations] Let R be an equivalence relation on a set A. Prove that if…

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Q: Define bounded set. Give an example of a set which is bounded below but not bounded above

A: Define bounded set. Give an example of a set which is bounded below but not bounded above

Q: Equivalence relation of

A: Let A = {0,1,2,3...} and define  relation  R = {(m, n); m^3 ≡ n^3 mod 3} we need to show that R…

Q: True/False: The relation R = {(a, a), (a, b), (b, a), (b, b), (c, c), (a, c), (b, c), (c, b), (d,…

A: The given set is                         S = { a , b , c , d }  and the given relation is…

Q: Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that R ∪ S is…

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Q: I) We know that -5,-4,-3,-2,-1? and IN are well-ordered sets with respect to the trivial ordering.…

A: Solution: Given the sets -5,-4,-3,-2,-1 and ℕ are well-ordered with respect to the trivial ordering.…

Q: True or False? 7. If A and B are two sets such that A ∪ B = A ∪ C then B = C.

A: Given: If A and B are two sets such that A ∪ B = A ∪ C then B = C.  We check that it is true or…

Q: Question Prove that if A and B are sets, then (ANB) U (ANB) = A

A: Venn diagrams of sets: Venn diagram of sets basically represents the relation between the sets in…

Q: 1. |(0,4) |-5, 3) |(1, 1) |(1, -3 -5 -5 Set of ordered pair: Domain: Range: Kind of Relation:

A: Since you are asking multiple questions. We are answering only the first question for you. We have…

Q: I) We know that -5,-4,-3,-2,-1 and IN are well-ordered sets with respect to the trivial ordering.…

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Q: undamental set

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Q: Challenge Problem. Let R be a equivalence relation on the set A. Define the relation R on set A x A…

A: i have used the definition of equivalence relation that is if relation is reflexive , symmetric and…

Q: cercise 2. Give an example of a relation R on A = {1,2,3} that is neither reflexive or irreflexive.

A: Given A = {1, 2, 3}

Q: {cat, dog, bird, rat} and R be a relation on A defined by :x and y have at least one letter in…

A: 2. a. First we now write the relation on A as form of matrix as follows which is also the adjacency…

Q: A={1,2,3,4} & R={(1,1),(1,2),(2,1),(2,2,),(3,4),(4,3),(3,3),(4,4)} Determine  Equivalence…

A: It is given that,  A = {1, 2, 3, 4}  and  R = {(1, 1), (1, 2), (2, 1), (2, 2), (3, 4), (4, 3), (3,…

Q: math question Let the relation R on X = {1, 3, 5, 6, 8, 9, 11} be such that xRy means “x − y is a…

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Q: (a) Using implication table obtain equivalence classes.

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Q: Definition: A set X C R is said to be disconnected if there exists disjoint open sets U and V such…

A: Given the function, f:ℝ→ℝ and the set X⊆ℝ is connected. To show that f(X) is connected: Suppose that…

Q: intersection graph of a collection of sets A1, A2,... , An is the graph that has a vertex for each…

A: Given sets: A1=0,2,4,6,8A2=0,1,2,3,4,A3=1,3,5,7,9A4=5,6,7,8,9A5=0,1,8,9