For each of the relations ~ on the integers ~ is relation, explain your an equivalence following whether L I ~ is an equivalence relation give an explict decription of the set of equivalence classes 2/2 @x~y if and only if x ≤ y 1 x ~ y if and only if X-y is. even

Q: 3. Let the relation R on X = {1,3,5, 6, 8, 9, 11} be such that xRy means "x – y is a multiple of 3".…

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Q: Let A = {1, 2, 3, 4, 5, 6} and let S = P (A), 1 set of A. the power a. For a, b e S, define a ~ b if…

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Q: Let A be a nonempty set and let ~ be an equivalence relation on A. Prove each of the following: (a)…

A: 11. Let A be a nonempty set and ~be an equivalence relation on A. (b)  We know that for each a, b∈A…

Q: ~ Define an equivalence relation on Z by a b if a - b is even. Show that . equivalence relation.…

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Q: Given the sets A = {a, b, c, d}, B = {0, 1, 2, 3} construct a relation R such that R is an injective…

A: There are two question , one is related to relation and function , second is related to equivalence…

Q: How many equivalence relations on the set {1, 2, 3}?

A: Given A=1,2,3 we know that a relation is said to be equivalence relation if it is reflexive,…

Q: is the following relation a functic {(1, 5), (-1, 7), (1, 8), (-4,9)} yes no

A: 1, 5, -1, 7, 1, 8, -4, 9.

Q: PROVE THAT IF A RELATION X ON NON EMPTY SET B IS REFLEXIVE AND TRANSITIVE THEN THE RELATION X…

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Q: NXN set on " (a,b)~ (c,d) -) a+d -b+c %3D define d as, equiualence relation? Shaw Is reation ""

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Q: Let S be the set of all ordered pairs of non-negative integers. Let R be a relation defined on A…

A: We have to find the equivalence of the given function and we are also given with the set in which…

Q: We have defined the relations ≡6 and ≡10 to be certain subsets of Z^2 . Their intersection R =…

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Q: ' (a,b) ∼ (c,d) ⇔ a+d =b+c '' defined as '∼' relation is that a equivalence relation?

A: It is equivalence relation if (a, b) belongs to ZxZ

Q: The congruence modulo 5 relation is an equivalence relation on the set {0, 1, 2, 3, 4, 5, 6, 7,8,9,…

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Q: Define the relation ~ on the set Z of integers by m~n if and only if m^2 = n. Show that ~ is not…

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Q: How can I prove that the relationship r^2 is a subset of r using the definition of composition?

A: The objective of this question is to prove that if r is a transitive relation on a set A, then r^2…

Q: 5. Let a and b be real numbers, not both zero. For (71, y1) and (12, 42) in R², set (11, yı) ~ (12,…

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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: efine the relation ~ on the set N of positive integers by a~b if and only if  a = b(10^k) for some…

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Q: Let the relation - on the natural numbers N be defined as follows: if n is even, then n ~ n + 1; if…

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Q: A relation ~ is defined on the set of all pairs of integers by the formula (m,n) ~ (u,v) m - An =…

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Q: Let R=}(x,y)|2 divides 8x+by} be a relation the Set H= {1, 2,3.4,5, 6. 10 Determine whether the…

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Q: 9. The relation ~ defined on the set of natural numbers by a ~ b means 'a – b is even is : A. an…

A: Equivalence relation : A relation which is reflexive, symmetric and transitive is an equivalence…

Q: tiv Consider the relation defined on Z by m~n if and only if m+n is eve (a) Show that ~ is an…

A: Consider the relation ~ defined on Z by m~n if and only if m+n is even. Now, To show  Relation ~ is…

Q: For set S = {1, 2, 3, 4}, we define the following relations R1 = {(2,2), (2, 3), (2, 4), (3, 2), (3,…

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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: Consider following relations on the set of positive integer: R₁ = {(a,b) | a> b} R₂ = {(a,b) | a = b…

A: The objective of the question is to determine which of the given relations are symmetric and…

Q: Equivalence relations "are" partitions. Let S be a set, and RC S × S be an equivalence relation on…

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Q: Define the relation ~ on the set R of real numbers by x~y if and only if x = -y. Show that ~ is not…

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Q: Let R be the relation defined on Z by aRb if a + b is even. I have the following equivalence classes…

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Q: A relation R is defined on the set of natural numbers N={1,2,3...}  as follows: aRb means "b=a+6/a;…

A: Domain means all the values that can be taken so that the aRb is defined.

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: Consider following relations on the set of positive integer: R₁ = {(a,b) | a> b} R₂ = {(a,b) | a =…

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

A: The objective of the question is to understand how the equivalence classes for the given equivalence…

Q: defined are the relations ≡6 and ≡10 to be certain subsets of Z^2 . Their intersection R =…

A: A relation R on a set X is a subset of X×X. That is R⊆X×X. (b). Let ≡6 and ≡10 are two subset on the…

Q: Exercises 1-10, determine whether the given relation is an uivalence relation on (1, 2, 3, 4, 5). If…

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Q: Let A # 0 be a set. Prove that A? is an equivalence relation on A.

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Q: Which of these ordered pairs belongs to the "does not divide" relation on the set of positive…

A: Which of these ordered pairs belongs to the "does not divide" relation on the set of positive…

Q: 6. Consider the set R2 and relation~: (1, 1)~ (2, 2) if and only if x2 = ₁ + m and y2 = ₁ +n for…

A: We shall solve only the first and second part of the question. If you want to solve the remaining…

Q: 1(b). Is (p->q)->[(p->q)->q] a tautology? Why or why not?  (c). Given the relation on the set .…

A: We are entitled to solve only one question at a time. Please submit another question separately. To…