LeA R be the relation defined the se4 Nx Z that (xy)EIC on so if and only if a) What is. the domain and Cange.

Q: Let R be a relation that is symmetric and antisymmetric. Show that R is transitive

A: Let R be the relation which is symmetric and Anti-symmetric.We will show that R is transitive, that…

Q: Is the relation R on X is reflexive, symmetric, weakly antisymmetric, antisymmetric, transitive?…

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Q: How many elements are in the Cartesian product U x V? * Let U = {u is odd | 9 < u < 14} and V = {v €…

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Q: The relation R on X={1,2,3,4}defined by (x,y) € R if x=y.

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Q: Let S be set of all strings of a's and b's. Define a relation R on S as follows: Vs, t E S, sRt e…

A: Let A be any and let R be any binary relation on the set A. Relation R is symmetric if for a, b∈R,…

Q: Consider the following relation R on R: (x, y) ER if and only if y E Q. What are the properties of…

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Q: ist the ordered pairs in the relation R from A = 0, 1,2, 3, 4, B = 1,2, 3, 4, 5, where Ris defined…

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Q: Let R be a relation from Q to Q defined by R = {(a,b): a,b ∈ Q and a – b ∈ Z}. Show that:(i) (a,a) ∈…

A: i) Given that a ∈ Q  a-a=0 ∈ Z So, (a,a) ∈ R for all a ∈ Q (proved)

Q: The relation R defined on a set A is antisymmetric if (a, b) ER = (b, a) E R for (A) Every (a, b) ER…

A: A relation R is said to be antisymmetric if (a,b)∈R and (b,a)∈R implies a=b

Q: Let R be the relation defined on P({1,., 100}) by ARB if and only if |AU B| is even. Is R reflexive?…

A: Given:  R is a relation defined on P 1, 2, … , 100 by A R B  if and only if A ∪ B is even. We have…

Q: Let R be the relation defined on Z by aRb it a+b is even Find the number of distinct classes? Select…

A: aRb if and only if a+b is even. a and b are integers. Hence, Either a and b both are even or both…

Q: Let A={a,b,c,d,e}. Find a relation R on A which is symmetric and transitive but not reflexive

A: Reflexive relation means every term of a set is related with itself

Q: Let R be the relation on N defined by R = {(n, m) EN x N: m=n+1). Then R is surjective. True False

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Q: Let X = {6, 7, 8, 9} and let the relation R on X be given by R = {(x, y): 3z e N₂ x + z = y}, where…

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Q: Consider the following relation R on R: (2, y) € R if and only if Va - y E Q. What are the…

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Q: Consider the relation R = {(1, 2),(2, 1),(2, 3),(3, 4),(4, 1)} on {1, 2, 3, 4}.Is R symmetric? Is it…

A: R=1,2,2,1,2,3,3,4,4,1set=1,2,3,4

Q: (a) Prove the following relation: B(x + 1, y): B(x,y) x + y %3D

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Q: Let L be the set of all lines in XY plane and R be the relation in L defined asR = {(L1, L2) : L1 is…

A: Line L is parallel to itself. This means L is parallel to L.So, (L,L)∈RSo, R is reflexive.

Q: b) A function g: Z → Zis defined by the rule g(m, n) = m + n Determine whether it is onto or not..

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: If a relation R on a set A is antisymmetric, then R is not symmetric.

A: To determine whether the given statement is true or false.

Q: Define a relation C from R to R as follows: For any(x, y) ∈ R × R, (x, y) ∈ means that x2 + y2 = 4…

A: Topic = function

Q: Let S = { (x, y) | x, y ∈ R} and relation R on S defined by (x,y) R (p,q) if and only if x-p = y –q…

A: Let S = { (x, y) | x, y ∈ R} and relation R on S defined by (x,y) R (p,q) if and only if x-p = y –q…

Q: R. I relations on A.

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Q: Let L be the set of all lines in a plane and R be the relation in L defined asR = {(L1, L2) : L1 is…

A: The given relation R is defined as follows.

Q: Let R be the relation on Z defined by    R = {(a,b): a, b ∈ Z, a – b is an integer}.Find the domain…

A: R = {(a,b): a, b ∈ Z, a – b is an integer}. We know that the difference of two integers is always an…

Q: Consider the relation R on R defined by (x, y) E R if and only if |æ – y| = ||x| – ly||- This…

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Q: Let R be the relation on Z given by R= {(a,b) : a < b}. %3D (a) Find R-1. (b) Find R which is Z x Z…

A: relation on Z.

Q: 5. Let R be a relation on R2 defined by (w1,y1)R(x2y2) if and only if yı +x1 = y2 + x2. (a) Is R…

A: Given relation is

Q: Let : [0, 1] → [0.c], te- and let w be a 1-form on R. What and foe, and why? is the relation between…

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Q: Let T be the set of all triangles in a plane with R a relation in T given byR = {(T1, T2) : T1 is…

A: Given, Let T be the set of all triangles in a plane with R a relation in T given byR = {(T1, T2) :…

Q: A relation R on a set A is called irreflexive iff (Vx E A)((x, x) ¢ R). It is called asymmetric iff…

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Q: Suppose that R is a symmetric relation. Match the correct term with each blank space in the…

A: Suppose  that R is a symmetric relation than prove that R-1⊆R Proof: Suppose that &lt;x,y&gt;∈R-1.…

Q: b) Let S = { (x, y) | x, y € R} and relation R on S defined by (x,y) R (p,q) if and only if x-p =…

A: We have S=x,yx,y∈R x,yRp,q  if and only if x-p=y-q   Reflexive property: A relation R is said to be…

Q: Part II: Prove/Disprove the following 2. Let R be the relation on Z, defined as follows: Vm, n e Z,…

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Q: Let A be the set of all lines in the plane. Define a relation R on A as follows. For every /, and /,…

A: Let A be the set of all lines in the plane . Define a relation R on A as follows For every l1 and l2…

Q: Given R = { (x,y) ϵ R | x = (y+1), x,y ϵ A } on A = {1, 2, 3, 4, 5}, which of the following…

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Q: Let G = (V, E) be a graph. Define a relation R on V ly: for all v, y EV, we have v, Rvy if and only…

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Q: 3. Let S = R × R and R be the relation on S defined by (a, b)R(c, d) iff a+c=b+d. Determine whether…

A: Reflexive: (x,y) R (x,y) As x+y=x+y Symmetric : if (a,b)R(c,d) then a+b=c+d. Since c+d=a+b then…

Q: Let R be the ternary relation on Z that is defined as R:= {(x,y, z) E Z × Z × Z : a² + y² + 2² < 5}…

A: If a relation is defined on Z, then the variables in the relation can have only integer values to…

Q: The relation R = {(x, y): x + y s 2x} is defined on the set of integers. Which of th %3D following…

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Q: 6. Define a relation from R to R as follows: For all (x, y) ER X R, (x, y) ER means that y = x2. a.…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: y if and only if x < 3y. Determine, plem B4: Consider the relation ~ on N defined by, x ~ proof,…

A: Given the relation ~ on ℕ defined by x~y if and only if x≤3y.   1) Reflexive: For any x∈ℕ, the…

Q: Using the relation (x – h) = h ando = E, P,(x)h', prove that Əx an xP'(x) – P'--1(x) = lP;(x)

A: The given relation: (x-h)∂ϕ∂x=h∂ϕ∂h    →    eqn 1 ϕ=∑pl(x)hl Substitute the value of ϕ in equation…

Q: 6. Give an example of a relation Ron A {-1,-3, -5} such that: (a) Ris both symmetric and…

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Q: Q/ if f contineous map Prove that f(B) ≤ f(B), VBsy

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Q: - Use the connectivity relation Mg- MR V M V M to find the transitive 2. closure of the following…

A: To find- Use the connectivity relation MR* = MR ∨ MR2 ∨ MR3 to find the transitive closure of the…

Q: 2. (MS) Consider the relation R5 on P({0,1,2,3}) such that (A, B) e Rz if and only if |A| = |B|.…

A: Since you have posted multiple questions and we can answer one question. So, answering the first…

Q: Define a relation R from R to R as follows: For all (x, y) ER×R, (x, y) eR if, and only if, x = y? +…

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Q: Let R be the relation on the set A(1,2,3) defined by R-((1,1),(1,3),(3, 1).(3,3), then RORR…

A: It is given that R is the relation on the set A=1, 2, 3 such that  R=1, 1, 1, 3, 3, 1, 3, 3. We have…