Problem A £2 points). Complete the definition of an equivalence relation by filling in the two blanks: A relation ~ on a set S is called an equivalence relation if 111111 •x~y⇒y~x, for all x, y ES 22 Y and Y~2⇒ for all x, y, z ES

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Q: For each relation, indicate whether the relation is: • Reflexive, anti-reflexive, or neither •…

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Q: Let W be the set of words in the English language. Define a relation R on W by W₁ R W₂W₁ and we have…

A: We are given that,      w1 R w2  <=> w1 and w2 have a letter in common.  Now, it is obvious…

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Q: 4. Let R be a relation defined on the set of integers by a R b if a +b = 0 or a – b = 0. Determine…

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Q: prove why each relation has or does not have the properties: reflexive, symmetric, anti-symmetric,…

A: The given relation R is as follows. R=x,y∈Z×Z:x is a multiple of y If x,y∈R, we denote x related to…

Q: Which of the following relations are transitive? The relations are in bold. (Remember: A relation R…

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Q: Give an example of two equivalence relations R and S on

A: Consider that R and S are equivalence relations on A=1, 2, 3.

Q: ame programs. A = the set of all people in the Social Security database; a Rb if and only if a and b…

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Q: Let S be the set of ordered pairs of positive integers, and define (a,b) R (c,d) to mean that 2a-d =…

A: A relation R is transitive on a set A if xRy and yRz then xRz for all x,y and z belong to A. Now,…

Q: 1. In the diagram below, there are 9 points and 8 lines: (a) Let be the relation between the points…

A: Given, In the diagram below, there are 9 points and 8 lines. a) Let ⋄ be the relation between the…

Q: 2 = y. Select the description that accurately describes The domain of a relation R is the set of…

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Q: A car dealership sells cars that were made in 2015 through 2020. Let the cars for sale be the…

A: Given:-               A car dealership sells cars that were made in 2015 through 2020. Let the cars…

Q: 1. Verify that the relation ~ is an equivalence relation on the set S given. (a) S = R reals, a ~ b…

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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: lation. Justify why your answers are corre R is a relation on the set of all people sue R is a…

A: EQUIVALENCE RELATION: If a relation R on a set A satisfies the following three criteria, it is…

Q: The relation R defined on Z by aRb if 3 | (2a + 7b) is an equivalence relation, I have the…

A: The relation  defined on  by  if  is an equivalence relationTo help understanding the equivalence…

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Q: Determine whether each relation is an equivalence relation. Justify your answer. If the relation is…

A: According to the given information it is required to check whether the given relation in each part…

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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: Define a binary relation on the set S=(-3, -2, -1, 1, 2, 3} as follows: R= {(a,b) ab>0} %3D a. Find…

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Q: An ordering on a set F is a relation, represented by ≤, with the following three properties:(o1) For…

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Q: A relation R is called atransitive if aRb and bRc implies cRa. Show that R is reflexive and…

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Q: 4. For each relation R below, determine whether it is an equivalence relation on the given set A.…

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Q: 2. (p.214, #6) There are five different equivalence relations on the set A {a,b,c}. Describe them…

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Q: Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that RUS is not…

A: 6 Given set is A=1,2,3. Consider the relation R and S on A is given by  R=1,1,2,2,3,31,2,2,1 And…

Q: Let A = {-6, -5, -4, -3, -2, -1, 0, 1, 2, 3) and define a relation R on A as follows: For all x, y…

A: Given : A = {-6, -5, -4, -3, -2, -1, 0, 1, 2, 3} and R is an equivalence relation on A defines as ;…

Q: The relation R defined on Z by aRb if 3 | (2a + 7b) is an equivalence relation. the equivalence…

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Q: The domain of a relation R is the set of real numbers. x is related to y under relation R if…

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Q: To find an equivalence class of x ϵ X determined by the relation R ⊆ X ⨯ X, R must be an equivalence…

A: Equivalence Relation: A relation R in X is called an equivalence relation if it is reflexive,…

Q: For the set A = {are, bot, cab, era)}, define the relation R on A to be: (x,y) eR if and only if…

A: As per the condition, in every order pair there should be only 1 letter in common.