Let R = {(0, 0), (1, 1), (-1, -1)} be a relation on set A. Deduce the rule between x and y for order pair (x, y) belong to R. %3D O a. R= {x, y) : y =x³ } O b. R= {x, y) : x =y²} O c. R= {x, y) : y =2x -3 } O d. R= { x, y) : x =2y -2 }

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

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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: . Define a relation R from R to R as follows: For every (x, y) ERX R, (x, y) E R means that y = r.…

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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 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 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: Vx E X, (x, x) ¢ R. X = {1,2,3}, h of the following relations R on X is irreflexive?

A: Here given set   X={1,2,3}   we know that relation is irreflexive when each x belong X (x,x) dose…

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: Let w = f(x, y), x = g(s, t), and y = h(s, t), where f, g, and h are differentiable. Use the…

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Q: Let f : A → B be an injective function, a be an order relation on B and 3-1 = {(x, y) E A x A :…

A: An order relation means the criterion of comparison between objects, that satisfies the properties…

Q: A. Let R be a relation on set A. A={x :xeJ and 0 sx s 12), and R={(a,b) : la - b| is multiple of 4}.…

A: Since not particular question asked, as per guidelines solution to only first question(i.e A) is…

Q: 4) B. Let A = {u, v, w}, B = {x, y, z}. Determine whether the relation R = {(u, x), (v, z), (w, y)}…

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Q: 1- R1 = {(A, B) E P(X) × P(X)/A S B} 2- R2 = {(A, B) E P(X) × P(X)/AN B + 0} %3D

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Q: (b) Let R= {(x,y) E R × R : 1 < x < 4 or x = 6}, %3D and S = {(x, y) E R × R: –1< y < 1}. i. Find…

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Q: Let R be the relation defined by x R y x² < y² Determine if R is an order relation on N? on Z?…

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Q: IS a function.. (b) Let R= {(x,y) € R × R : 1 < ¤ < 4 or x = 6}, %3D and S = {(x, y) E R × R : –1 <…

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Q: 3(a) Consider the relation R defined on the set X={a,b,c,d} and Y={1,2,3,4} from X to Y, where R=…

A: The objectives are: i) Deduce the matrix complementary relation MRC ii) Find the value of TCoR-1

Q: For each n E N, we write S" := {(x1, x2, ..., In+1) E R"+1 : E? = 1}. (1) Let f : S2 → Rª be the…

A: Given: Sn:=x1,x2,...,xn+1∈ℝn+1:∑i=1n+1xi2=1 for each n∈ℕ f:S2→ℝ4 is the function defined by…

Q: 9. Let X = {r1,12, 23, T4}, Y = {yı,y2, Y3}, and Z = {zı, z2}, Let R be the relation from X to Z…

A: Given: 9) X=x1, x2, x3, x4, Y=y1, y2, y3 and Z=z1, z2, z3. R=x1, z1, x2, z2, x3, z1, x3, z2 and…

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: Relation

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

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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: Consider the relation R defined on the set X={a,b,c,d} and Y={1,2,3,4} from X to Y, where R= {(?,…

A: Disclaimer: Since you have  asked multiple question ,we will solve first question for you . if you…

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: 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: Given the map f:R3 R4 defined by f(x,y,z) = (0,0,0,0) then rank of f is:

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Q: Α) Reflexive (No), symmetric (No), transistive (No) Reflexive (Yes), symmetric (Yes), transistive…

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Q: Let T = {0, 1, 2, 3} and the relation R is defined on T as follows: R = {(0, 1). (1, 2), (2, 2)}:

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Q: The domain of the function f(r, y, z) = In(6 2xy) is O {{z, y, z) E R³ ° : ay > 3} O {{z, y, 2) E R°…

A: see below the answer

Q: Define a relation S from R to R as follows: For every (x, y) ER X R, (x, y) E S means that x> y. a.…

A: (a)It is given that the relation S from R to R is defined as for every (x, y) ϵ R × R, (x, y) ϵ S…

Q: .The table below shows corresponding values of x and y which approximately satisfy a relation of the…

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Q: Let Z be the set of all integers and R a relation on Z defined R= {(x,y) E Z × Zx = y +1}.Which of…

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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: Discrete structure

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Q: Let R be a relation on the set A = {a, b, c, d} described by the matrix MR=(1 0 0 1          0 1 0…

A: We will use the given matrix to write R in the ordered pair form and then we will find domain and…

Q: Let f(x, y, z) = x2 (e)^y/z. Compute f(-1, 0, 1), f(1, 3, 3), andf(5, -2, 2).

A: Let fx,y,z=x2eyz 1. we have to compute f(-1,0,1) as, fx,y,z=x2eyzHere x=-1, y=0,z=1f-1,0,1=-12e01=1…

Q: Is anyone of the veetors e. 2-, ERa linear combination of the others? If so, find the relation(s)…

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Q: The domain of the function f (x, y, z) = In(6 – 3ry) is - o {(x, y) E R² : xy > 2} O {(x, y, z) E…

A: Please refer to the image below

Q: 2. The table below shows corresponding values of x and y which approximately satisfy a relation of…

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Q: (b) Let R= {(x, y) E R × R : 1 < x < 4 or x = 6}, and S = {(x,y) E R × R : –1< y < 1}. i. Find the…

A: Solution: The given relations are R=x,y∈ℝ×ℝ : 1≤x≤4 or x=6 and S=x,y∈ℝ×ℝ : -1&lt;y&lt;1

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

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Q: Exercise 1 find the relation Ship between PeSIstarce IC furrent) from the table below, VAR 1 2-28 10…

A: Given that  R V I 2 1.2 0.6 4 1.42 0.355 6 1.61 0.268 8 1.83 0.229 10 2.10 0.219 12…

Q: Ris a relation defined from Z = {...,-2,-1,0, 1,2,...} to Z by , y E Z, xRy + x+y= 100 Choose the…

A: Given that R is a relation defined from Z={...,-2,-1,0,1,2,...} to Z by      ∀x,y∈Z, xRy⇔ x+y=100.

Q: Let R be a relation on the set A = {1,2,3,4,5, 6} defined by R = {(a,b) E A x A| a + b < 9}. a. List…

A: A ={1,2,3,4,5,6}

Q: Let S = {(x,y) : x, y € R} = R². Define an equivalence relation on S (i.e. a subset of S × S = R² ×…

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Q: Let A = (0, 1, -1, 2} , R relation on A defined by R = {(a, b) : b= a², a, bE€ A}. Write R. %3D

A: Given ,  Let A = {0 , 1 , -1 , 2}  R relation on A defined by  R = {(a , b) : b = a2 , a , b € A} We…

Q: The adjacency matrix for the relation R on {v1, v2, v3, V4} is given below. 1 0 1 1 0 0 1 1 1 1 1 1…

A: Given the adjacency matrix for the relation R on the set A=v1, v2, v3, v4 as,…