Let No = (NU{0}) be the set of natural numbers including 0. Let M = N = (No x No × No): relation - on M x M is defined as I~y (a, b, c) ~ (d, e, f) = a +b+c=d+e+f a) Prove that ~ is an equivalence relation. b) Determine all elements of the equivalence class (1,0, 1). c) Let z = (a, b, c) E M and y = (d, e, f) E M. the relation < on M x M is defined as follows: %3D I< y (a, b, c) < (d, e, f) 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: Let R = { (1,1), (3,1), (2,1),(2,2), (1,3) } be a relation on the set A = {1,2,3}. (a) Determine…

A: Explanation of the answer is as follows

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

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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: ' (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: Give a specific reason why the following set R does not define an equivalence relation on the set…

A: We will find out the required value.

Q: Let R be an equivalence relation on A = {0, 1, 4, 5, 7, 9} and R = {(0, 9), (9, 0), (0, 0), (9, 9),…

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Q: Let a relation ∼ on R2 = {(a, b): a, b ∈ R} be defined as: (a, b) ∼ (c, d) if and only if | a | + |…

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Q: Let ~ CX *X be an equivalence relation on a set X. For x EX define x := := {x |x E X} is a partition…

A: This is a question from Relation.

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: 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…

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: Use Newton's method to find a solution accurate to within 10^-4 for x^3+3x^2-1=0, [-3,-2]

A: Solution to the given equation is -2.8794  Thank you  Let me know if you have any doubts…

Q: (3) Let S be the equivalence relation on (0, 1, 2, 3} x {0, 1,2} defined by (a, b)S(c, d) if and…

A: From the given information. “S” is an equivalence relation on {0,1,2,3}X{0,1,2}. The equivalence…

Q: What are the equivalence classes of the equivalence relations on {0, 1, 2, 3}?

A: Answer:-  Find the equivalence classes of the equivalence relations on A = {0, 1, 2, 3}?

Q: Let be the equivalence relation on Z defined by z~ y if and only if z-y is divisible by 15. Give…

A: Equivalence relation

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

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Q: 6. Let (a, b), (c,d) E R2. Define a relation ~on R2 by [ (a, b)~ (c,d) if |ab|=|cd| Show that is an…

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Q: 1. Which of these relations on {0, 1, 2, 3} are equivalence relations? Determine the properties of…

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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 the relation R on the set Z be given by the condition: (x, y) E Rif and only if x4 = y4. Answer…

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Q: 1) Let R be the relation on Z+ such that (p, q) R(r, s) if and only if p- s = q ·r. That is, the…

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Q: consider a relation R={(a,b)|0<=a-b<=1} on a set A={0,1,2,3,4} a) Describe R using masters method…

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Q: Which of these relations on (0, 1, 2, 3} are equivalence relations? o {(0, 0), (0, 1). (0, 2), (1,…

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Q: Decide whether the following relations is a partial order or not. (a, b) | a Í b, a and b are…

A: We have to decide whether given relation is partial order or not?

Q: Lex 172,3,4). Consider the relation R on X defined as follows. R = ((1.1), 13), (2,2), (2.4), (3,1),…

A: I have solved both subpart using basic definition of equivalence relation and equivalence class.

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Q: 4- The orthogonal relation is A: symmetric and reflective relation B: symmetric and not reflective…

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Q: Let R be the relation on a set {1,2,3,4,5} containing ordered pairs (1,1),…

A: A relation R is called reflexive on a set A if (x,x) is in R for all x in A. A relation R' is called…

Q: Let R, S, and T be sets. Let f: R -» S, and g: S -» T be maps. Assume we know that qf is 1-1 Must f…

A: Given: