5. Let a and b be real numbers, not both zero. For (71, y1) and (12, 42) in R², set (11, yı) ~ (12, y2) → a(11 – 12) + b(yı – y2) = 0. (a) Show that - defines an equivalence relation. (b) Identify the equivalence classes.

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Q: Prove that the relation of congruence is an equivalence relation.

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Q: 2 1-Find the geometric location of the relation z – 3 -ži = v2. 3

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Q: 4. Let R be the relation in the positive integers

A: 4. Given, R be the relation in the  positive integers ℕ defined by                        R=x, y: x,…

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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: Describe the equivalence classes of the relation R = {(a, b) : a € Z, b E Z, 13 divides (a – b)}

A: a equivalence class is a subset of the set on which the relation R is defined such that all elements…

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Q: Assume (r1, y1) ~ (x2, Y2) → f(x1,Y1) = f(x2, Y2). Prove that ~ an equivalence relation.

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Q: a) Prove that R is an equivalence relation. b) Find [C] for C = {1, 3}. ) How many different…

A: Follow the answer below.

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A: partial order means reflexive and antisymmetric.

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Q: The domain of relation R is ZxZ. (a, b) is related to (c, d) if a s c and b s d. Which statement…

A: In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and…

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Q: For the points (x1, y1) and (x2, y2) in the plane R?let (x1, y1)~ (x2,Y2) mean that xỉ + yỉ = x + y…

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Q: consider the relation R={(1,a),(1,b), (3,b),(3,d), (4,b)} form X={1,2,3,4} and Y={a,b,c,d}. Thus…

A: Consider the relation

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Q: 5) Compute the number of ordered pairs (x,y) with x>0 and y>0 that satisfy x+(y)=5.3 and y+(x)=5.7

A: In this question we have to find the number of ordered pairs (x,y).

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A: According to question,We have to discuss about reflexive, symmetric, transitive relation.

Q: 2|A:k||2|| Bx:||2) < || |||B||F k%3D1

A: Please check the answer in next step

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Q: Let R = {(f, g) | f(1) = g(1)} be a relation defined on the set of func- tions from Z to Z. Is R an…

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A: Given problem is :

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Q: 13. Let R C R XR with {(x, y)|x2 =, y?}. Characterize R in terms of whether it is reflexive,…

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Q: Prove that the following relation is equivalence relations and prepare it in latex: On R, with x∼y…

A: Revision : A relation ~ defined on a set  A is an equivalence relation if and only if it satisfies…

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A: Given relation xy≥1, where x,y are on the set of all integers

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Q: For universe S = R², define relation ~= as: (a,b) ~= (c,d) < 2a - b = 2c - d Prove that ~= is an…

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Q: 3. Use the cross product properties to prove the relation (a - b) × (â+b) = 2(â × b) given a = (1,…

A: Given,a=i-3j+2kb=-2i+0j+k

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Q: Explain why consimilarity is an equivalence relation on M,.

A: Given that consimilarity is an equivalence relation on Mn.

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A: Either show the following relations on {0, 1, 2, 3} is an equivalence relation,

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.