Let A = {1, 2, 3}. Then number of equivalence relations containing (1, 2) is. Chose the correct.(A) 1 (B) 2 (C) 3 (D) 4

Q: 9.32. A relation Ris defined on the set A = {a+bv2: a,b € Q, a + bv/2 + 0} by x R y if æ/y E Q. Show…

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Q: List the ordered pairs in the equivalence relations produced by these partitions of (0, 1, 2, 3, 4,…

A: Solution: If P=A0,A1,.....,Ak be a partition of a set A then the partition generates an equivalence…

Q: Every equivalence relation is reflexive. True False

A: A relation is said to be an equivalence relation if and only if the relation R is reflexive,…

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: 2. If A = {1, 2, 3} and B = {2, 3, 4}, and R is the relation on AxB defined by xRy when x + 2y is…

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Q: 1. Find all equivalence relations on{1,2,3}.

A: Given set is, 1,2,3

Q: 9.5. For the relation R= {(1,1),(1,2) , (1, 3) , (2, 2) , (2, 3) , (3, 3)} defined on the set {1,…

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Q: (a) Ri (b) R2= {(1,2), (1,3),(1,4),(2,2),(3,3),(5,3),(5,4),(5,2)} /hich of them is an equivalence…

A: Any relation is equivalence relation if satisfy the following conditions where is set of elements a)…

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: What property is NOT included for an EQUIVALENCE RELATION? * O Reflexive O symmetric O Transitive O…

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Q: 4. For (1, yı) and (r2,y2) in R² we set (11. yı) ~ (12. Y2) →{+ =3+ yi. (a) Show that ~ defines an…

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Q: Let A = {a, b, c, d} and R = {(a, a), (b, a), (b, b), (c, c), (d, c), (d, d)}. Determine whether the…

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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: Let A = {a, b, c, d, e, f,g, h}, and let G and H be the following equivalence relations in A: %3D G…

A: Given that A = a , b , c , d , e , f , g , h . Also,  G and H are the following equivalence…

Q: Let A = {1,2,3,4, 5, 6} and let R be an equivalence relation on A. Suppose that 1R2, 3R5 and 6R3.…

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Q: 22) (a) Show that the relation {(0,0), (1,1),(1,2), (2,1), (2,2), (3,3)} is an equivalence relation…

A: Given 0,0,1,1,1,2,2,1,2,2,3,2

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: Show that the number of equivalence relation in the set {1, 2, 3} containing(1, 2) and (2, 1) is…

A: To show:The number of equivalence relation in the set {1, 2, 3} containing (1, 2) and (2, 1) is two.

Q: Let Let A={2,4} and B = {1,3,5} and define relations U, V, and W from A to B as follows. For all (x,…

A: Given that -  Let A={2,4} and B = {1,3,5}

Q: 2. Determine the partition of B = {1,2,3,4,5,6,7,8,9,10} induced by the equivalence relation B…

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Q: Prove and say the name of the following equivalence relation x ~ y ⟺ x - y = 4k, k ∈ Z

A: x ~ y iff x - y = 4k , k in Z Implies that  x is congurent to y mod 4.

Q: ii. Determine whether the relation, R = {(1, 3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)} is: Yes/No…

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Q: Suppose A = {-4,-3,–2,–1,0,1,2,3,4} and R is defined on A by aRb a² - b² is divisible by 4. Prove…

A: A relation R on a set A is said to be an equivalence relation, if it satisfies the following three…

Q: Define the relation∼ on Nby m ∼ n if and only if the sum of the distinct primes that divide m is the…

A: To test if the given relation satisfies the conditions for reflexivity, symmetry and transitivity

Q: a) Let A = {4, {$}, ($, [$}}} and B = {1,2}. How many equivalence relations on A?

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Q: Let R ⊆ ℝ×ℝ with R={(x,y)|⌈x⌉=⌈y⌉}, that is, x and y round up to the same number. Characterize R in…

A: Given problem is :

Q: Let A = {2,4,6,8,10}. The distinct equivalence classes resulting from an equivalence relation R on A…

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Q: How many symmetric relations on the set A = {1,2, 3, 4, 5, 6, 7, 8} contain the ordered pairs (2,…

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Q: Essentials of DISCRETE MATHEMATICS   Q: Shot that the relation “congruency modulo n” is an…

A: We have to show that the relation “congruency modulo n” is an equivalence relation.

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: 6. Find all equivalence relations on {1,2,3}. 7. Show that for n, m ɛ Z+, gcd(2" – 1,2m – 1) =…

A: Note : We are entitled to solve only one question at a time and up to 3 subparts only. To find -…

Q: (d) Give an example of an equivalence relation on the set f1,2, 3} with exactly two equivalence…

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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: Which of these relations on {0, 1, 2, 3} are equivalence ?relations

A: Equivalence relations are the relations which are reflexive (xRx), symmetric (xRy implies yRx),…

Q: Give at least three different examples of equivalence relations.   Note: In every example please…

A: A relation R on a set A is said to be an equivalence relation if and only if the relation R is…

Q: How many equivalence relations on the set {1, 2, 3}? 1. О З 2. O 6 3. О 5 4. O 4

A: The objective is to find the total equivalence relation on set {1,2,3}.

Q: Which of these relations on {0,1,2,3} are equivalence relations or a partial order? Determine the…

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Q: Determine whether the given relations are partial order or equivalence relation on A = {1, 2, 3, 4,…

A: As per answering guideline, we can answer only one question at a time. Please repost other question…

Q: The number of equivalence relations on the set {1, 2, 3, 4} is

A: A relation defined on a non empty set S is called an equivalence relation if it is reflexive ,…

Q: 7. Let A = {1,2,3,4}x{1,2,3,4}. Define an equivalence relation ~ by (x1,x2) ~ (x3,xa) iff xxx2 =…

A: Let A=1,2,3,4×1,2,3,4. The equivalence relation ~  is defined by,        "x1,x2~x3,x4 only if…

Q: Let R C R+ x R+ with R = {(x, y)|[x] = [y]}, that is, x and y round up to the sane number.…

A: Given, R⊆ℝ+×ℝ+ with               R= x, y | x=y

Q: 6) Let A = {1,2,3,4}, show that by counterexamples that the following relations are not equivalence…

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Q: b) Write out, using set notation, the equivalence class for the point (0, 2)

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Q: Let A = {1,2,3,4} and let R = equivalence relation. Determine the equivalence classes.…

A: Given A=1,2,3,4 and R be the relation defined by R=1,1,1,2,2,1,2,2,3,4,4,3,3,3,4,4. We have to show…

Q: Find all equivalence relations on {1,2, 3}.

A: A relation R on a set A is said to be an equivalence relation if it is reflexive symmetric and…

Q: (b) Let R and S be two equivalence relations on X. Are RnS, RUS, R \ S, also equivalence relations…

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Q: Enter an example of an equivalence relation R on the set X = {0, 1, 5, 6, 8} such that all of the…

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Q: equivalence

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Q: What is equivalence relation

A: For a set A, a relation R defined on A is called EQUIVELENCE RELATION, if it is REFLEXIVE, SYMMETRIC…