4. R= {(x,y) x + y ≤ 8} reflexive irreflexive symmetric asymmetric anti- symmetric 1. 2. 3. 4. Which of the given relations is an equivalence relation? transitive intransitive

Q: Discrete math.  Let S = R. On S we define the relation R as follows (∀x)(∀y)(xRy ⇔ y ≥ x + 3). Is R…

A: The given set S=ℝ. The relation R defined in the set S is ∀x∀yxRy⇔y≥x+3. We have to check whether…

Q: All the possible relations on A {1,2,3} is equal to i. i. 8 relations 9 relations Non of these iii.

A: The number of relations on a set of n elements is given by 2n2.

Q: • if Rit is a symmetrical relationship then R-1 is not symmetrical False O true نقطة واحدة • ifA =…

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Q: 1. Let R be a relation on R x R such that (*1vi)Rs02) if and only if x,yı = x2y2. (a) Is (2,3)R(1,4)…

A: A relation from a set A to B is defined as a subset of A×B. Here R is a relation on ℝ×ℝ such that…

Q: R.2. Consider the relation R=- ={x,y):x.yeR&]x=}<3}. Is R an equivalence relation on set of real…

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Q: 7. (6 points) Let T be a relation defined on the set A = {1,2,3} such that T = {(1,1), (1,2), (2,2),…

A: The objective of the question is to determine whether the given relation T is reflexive, transitive,…

Q: b) Let X = (x, y, z). Then show that A = {(x,x),(y,y),(z,z)} is an equivalence relation. Determine…

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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: 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: 7. Suppose that R = {(x, y)|x + y <7}; R, is a relation from X to Y, R2 = {(y,z)|y = z + 1}; R2 is a…

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Q: 15- R {(x,y) EZ XZI(y-x) = even element} is an symmetric %3D 16- R {(x,y) EZXZI(y-x) = even element}…

A: Recall: Reflexive, symmetry and Transitivity:   Let R be a binary relation on a set A. R is…

Q: Consider the relation R on R, where R = {(a, b) | ab ≥ 0} . (a) Is the relation R reflexive,…

A: is a relation on

Q: Let R be a relation on R × R such that (,71)R¢xI2) if and only if xıyı = x2y2. -) Is (2.3)R(1,-6) a…

A: It is given that R be a relation on ℝ×ℝ such that Rx2,y2x1,y1 iff x1y1=x2y2 For part (a) According…

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: 2 Explain why the relation on N defined as is not an equivalence relation. {(x,y): +y is a multiple…

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Q: The relation p = ((a, b) e R x R: 1+ ab > 0} is %3D (a) reflexive, symmetric but not transitive. (b)…

A: Given relation is ρ =  a, b ∈ ℝ × ℝ : 1 + ab &gt; 0

Q: 1) Define a relation on the set of points in the coordinate plane by setting (x, y) <1 (x', y')…

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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: (i) Give an example of a relation S on A = {1,2, 3, 4} with S is reflexive, not symmetric and not…

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Q: 2 Relations For the following relation R over the integers, prove whether R is or is not: 1.…

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

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Q: Q.1 Explain why the following statements are false 1- The relation 1 2 3 4 a 1 0.1 0.2 b 0.1 0.3 0.1…

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Q: Please find a relation R that makes the statement true and a relation R(x, y) that makes the…

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Q: 17. Equivalence relations 1. Let X = {a, b, c, d, e, f} and R be the relation on X defined by R =…

A: The given relation is an equivalence relation. The equivalence classes are given below.

Q: Let < be a partial order on A. Assume that a,b EA are elements with the property that: for any X EA,…

A: (First part): Reflexive property : Since ≤ is an reflexive relation then for every element x∈A we…

Q: 9. For each of the following relations on N, determine which of the five properties are satisfied.…

A: We have to determine properties based on the given relations on ℕ

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: Let X = {x € Z+ | 15 < 4x < 22} and Y = {y is even | 0 < 2y + 1 < 15}. Define a relation R from X to…

A: A relation defines the relationship between sets of values of ordered Paris. The set of elements in…

Q: QUESTION 2 Define a relation on Nx N as follows: (a, b) R (c,d) a+d=b+c (2.1) Is (3,6) R (3,5)?…

A: We have to show that the given relation is an equivalence relation.

Q: Determine whether the relation is reflexive, symmetric, antisymmetric and transitive. Provide one…

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Q: Is this relation discrete or continuous? -50 -5 -5- O Discrete O Continuous

A: This relation is Discrete.

Q: Characterize the relations in questions 14 and 15 in terms of whether each is reflexive,…

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Q: 4. Let R be the relation xRy if 3| (x – y) on Z. Prove that R is an equivalence relation.

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Q: 1. State the domain of this relation. * 2 -2 {x ɛR} O {x ɛ R, x + 1} O {y ɛ R} O {y ɛ R, x + 1}

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Q: 7. 5 R 3? Is 2 R 8? Is 8 R 2? Define a relation R on Z by x R y if and only if x-y ≤ 3. Is 3 R 5? Is

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Q: Let A = {1,2,3}, X = {1,3}, and R is a relation on A, such that R= {(x,y) | x<y ^ x, y = A} R"X =…

A: , and is a relation on .

Q: It is based upon properties of relations. *Explanation is mandatory. Check whether the following…

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Q: R.5. Define a relation < on the set of ordered pairs of real numbers (x, y) as follows: (X:V1)< (x2,…

A: The relation ≺ is defined as follows:  x1,y1≺x2,y2 if and only if x1&lt;x2 or x1=x2 and y1≤y2