Discrete math Let S = Z × Z and define the relation R as follows (a, b)R(c, d) ⇔ ad = bc. Show that R is an equivalence relation and find the corresponding equivalence classes.

Q: 8. Define relation R on (Z+ U {0}) × Z+ by (a, b)R(c,d) if ad = bc. (a). Prove that R is an…

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Q: 4. Let f : X → Y define a relation on the set X by „Ry if and only if (x) = fy). Is f an equivalence…

A: f is an equivalence relation if f satisfies three properties. 1. if f is a reflexive relation  2. if…

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…

Q: Let S = R^2 2 and define the relation R as follows (x1, y1)R(x2, y2) ⇔ x1^2+y1^2 = x2^2+y2^2 Show…

A: We have to check all condition of equivalent relation  i.e. reflexive , symmetric  and transitive ,…

Q: R.3. Consider the relation R = {(m,n):m,n E N & m|n}. Prove that R defines a partial order on the…

A: A relation R is said to be partial order on a set X if the relation is reflexive, transitive and…

Q: Let~ be the equivalence relation on Z defined by ~y if and only if z Give three examples of elements…

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Q: 1. R is the relation defined on Z as follows: Vm, n € Z, mRn 5|(m² — n²). (a). Prove that R is an…

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Q: Prove that R= {(a, b) Ew² | 3 divides (b-a)³} is an equivalence relation on w

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Q: by xRy if and only if 7 divides x² – yʻ.

A: A relation is equivalence if it is reflexive,symmetric and transitive

Q: A relation R is defined on the set of integers by: aRb = a + b = 2m + 1, where m is an integer. Show…

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Q: Discrete Math Let S be a nonempty subset of Z and let R be a relation defined on S by xRy if 3 | (x…

A: Equivalence relation: A relation  on a set  is said to be equivalence relation on a set if it…

Q: If a relation is an equivalence relation, state the set of equivalence classes.

A: For the given relations To check the properties (i) Reflexive (ii) Symmetric (iii) Transitive.

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: 3. Define the relation R on Z by mR, if and only if 2|(m – n). Show that R is an equivalence…

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Q: Q5) Let X = {a, b,c, d} and let R = { (a, a), (a, b), (a, c), (b, a), (b, b), (b, c), (b, d), (d,…

A: Given : X = a, b, c, d R = a, a, a, b, a, c, b, a, b, b, b, c, b, d, d, d be a relation.   To show…

Q: Exercise: Let R be a relation on people such that (a,b) is" a is a parent of b Let S be a relation…

A: Let R be a relation on people such that (a,b) is "a is a parent of b".Let S be a relation on people…

Q: aRb, cRd and aRd, then bRc.

A: A relation R defined on a set A is i) reflexive if aRa for all a belonging to A.ii) symmetric if aRb…

Q: 2. Let A={-4,-3,–2,–1,0,1,2,3,4} and Ris a relation on A defined by: 31(m² –n°) mRn 4 (a) Show the…

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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: 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 U = {a, b, c, d, e}. Using a binary table define relation RCU x U such that R is symmetric but…

A: Given that, a set   , then by the Cartesian product  will be the sell of all possible ordered pairs…

Q: Discrete Math: Lets say B = {1,2,3,4,5,6}. Let R be the smallest equivalence relation on B which…

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Q: Let S be the set {a,b.c} and the relation R on S is…

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Q: Let A = {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3} and define a relation R on A as follows: For all m,…

A: Given set is A={-7,-6,-5,-4,-3,-2,-1,0,1,2,3} Also R is an equivalence relation on A, defined as…

Q: Let R be the relation, {(a, b) e N x N:a + 26 is divisible by 3}. Give an example that shows that R…

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