VII.3. Let Rbe the relation on {1, 2, 3, 4} given by r Ry if, and only if, æ – y = 0. Represent Rin the following ways: • as a set of ordered pairs; • in graphical form; • in matrix form.

Q: If R is a relation defined from the Set A ={ 6,12,25,36} to the set B = {3,4,5,6} as follows: {(x,…

A: Part (i):   Relation set of R in the roster form:

Q: 1. Suppose the relation R on {1, 2, 3, 4, 5} defined by (x, y) E R, if x² sy+20 (a) Write the…

A: Since you are asking multiple questions. As per our guidelines, we are supposed to answer only one…

Q: 7.1.4 A relation is defined on N by a Rb + ; E N. Let c,d E N. Under what conditions is it…

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Q: Question 4 (a) Let Ri and R2 be the relations on {a, b, c, d} given by R = {(a, a), (a, b), (c, d),…

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Q: (1 1 0\ 1 0 1 1 Draw the directed graph for the relation defined by the matrix 1 1 10 1/

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Q: Let A = {2, 3, 4, 5, 6, 7, 8} and define a relation T on A as follows. For every x, y Е А, хТу —31(х…

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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: Let A = {2, 4, 5}, and let R be the relation on A consisting of pairs of the form (a, b), where ab…

A: Pairs in R is: {(4,4),(4,5),(5,4),(5,5)} Only these have ab>12

Q: 2 1-Find the geometric location of the relation z – 3 -ži = v2. 3

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Q: 1. Suppose that the matrix representation of a relation is given by 11 1 1 0 1 1 1 0 0 11 0 0 0 1 MR…

A: A zero-one matrix is the matrix representation of a relation. The zero-one matrix is the matrix Mij…

Q: C. Let T be defined onN N by (a, b)T (c, d) if and only if a c and b 2 d. Write down the full nature…

A: We will use the basic definition of reflexive, symmetric, antisymmetric and transitive realtion.

Q: In this exercise, you want to show that a relation R C A? is transitive + R" C R for all n E N =…

A: In this problem, we have to show that a relation R ⊆ A2 is transitive if and only if Rn ⊆ R for all…

Q: Let T: R°→R be image of eath vestor reflection in Hhe x-qxis. Fnd the O (5, 3) O (4,-1) O 6 (4,0) O…

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Q: 9. Consider the following relation R on A where A = {1,2,3, 4, 5} %3D aRb < min(a, b) 2 1 For…

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Q: Create (a) the ordered pairs, (b) graphical representation, and (c) the relation matrix, for  the…

A: Given a relation R on the set B as "is factor of" B=1,2,3,6. a The ordered pair is…

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: A. Let R be a relation on set A. A={x: xeJ and 0 sxs 12), and R-{(a,b) : la - b| is multiple of 6}.…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: If R is a relation defined from the Set A = { 6,12,25,36} to the set B = {3,4,5,6} as follows: R =…

A: Since you have asked multiple sub-parts, we are answering the first three sub-parts for you now. If…

Q: 5. For the following directed graph, let E = {I,J,K,L, M} and let V = {a, b, c,d}. %3D a J L b K For…

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: Consider X = [1,2]? with the relation (x1, y1)~(x2,y2) if x1y2 = X2y1. Also define g: X [1,2] by the…

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Q: 15-18: Suppose we define a relation T from A = {-3, 2} to B = {-2, 0, 1} as follows: For all (x, y)…

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Q: Let A = {1,2, 3, 4, 5,6} and R a relation on A whose MR is given below 0 100 0 1] 0 0 10 0 0 00 1 10…

A: Let R be a relation on a set A. The relation R can be represented using the matrix and the digraph.…

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: 3. Determine whether the following sets in R° are linearly independent. 1 [2] 3 b. S = -2

A: We have to check

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: 3. Define a relation S from R to R as follows: For all (x, y) e R xR, (x, y) eS means that x2 y. a.…

A: Given x,y∈S  Mean x≥y    x,y∈R×R

Q: 4.4.4 List the relation on N defined bv h(x, y) e N x N : x > y } 9 Scanned with CS CamScanner as a…

A: The relation given is already a subset of the Cartesian product N x N. It can be written as follows.

Q: The matrix representation for the relation R on {v1, v2, v3, v4} is given below. The first…

A: We will use the concept of adjacency matrix to write the ordered pairs of the given matrix

Q: Define the following sets e and s as follows: e = {Devin, Elsa, Floyd}, s = {Software 1, Software 2,…

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Q: Suppose that the matrix representation of a relation is given by 1 1 11 0 1 1 1 0 0 1 1 0 0 0 1 MR…

A: Given that the matrix representation of a relation is MR=1111011100110001

Q: Given A = (1, 2, 3, 4) and B = (x, y, z). Let 7? be the following relation from A to B: R =…

A: To represent a relation from A to B in matrix form  is given by

Q: Determine whether the following graphs are isomorphic. Vị v2 V3 a) fi u2 el Is e3 e4 U4 f4 u Vs 5 f2…

A: To determine the given graphs are isomorphic or not.

Q: 4. Let G = {–2, 0, 2} and H = {4,6, 8} and define a relation V from G to H as follows: For all (x,…

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Q: Given X = {1,3,5}. R is a relation on X, defined by aR,b if and only if la – bl is an even integer.…

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Q: 8. Let A (2, 4) and B (1,3, 5) and define relations U, V, and W from A to B as follows: For all (x,…

A: Given that: A={2,4}B={1,3,5}

Q: Let C = {a, b, c, d}. Find a relation R on C that has exactly 3 ordered pair members and is both…

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Q: Suppose A = {a1, . . . , am} and B = {b1, . . . , bn}. Let R and T be relations from A to B with…

A: Let A=a1,a2,...,am and B=b1,b2,..,bn Let R:A→B and T:A→B are two relations. Let m and n be their…

Q: Compute the linear correlation coefficient between the two variables and determine whether a linear…

A: Solution: Correlation coefficient is given by, r=∑XY-nX¯ Y∑X2-nX¯2∑Y2-nY¯2 When the value of r is…

Q: Question. 2 Show that Span (x₁,x2,...,x,y) = Span (x₁,x2,...,xn) if and only if y is a linear…

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Q: Q5 (B) Let A = {1,2,3, 4, 5,7}. Draw the directed graphs associated with the following relations on…

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Q: In this exercise, you want to show that a relation RC A? is transitive + R"C R for all n E N = {1,2,…

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Q: 2. Let D be the set {xEZ I 2<x<7} and relation M on D defined by: xM y→x and factor AND x< y. y have…

A: Note:- As per our guidelines, we can answer the first three sub-parts of this problem. Please…

Q: In this exercise, you want to show that a relation RC A? is transitive + R" C R for all n EN=…

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Q: 0 0 represents the relations R defined on 1 1 c) The matrix M = 1 11 the set A = {1, 2, 3, 4}. i)…

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Q: [1 1 01 1 c) represents the relations R defined 1 The matrix M %3| 11 1. the set A = {1, 2, 3, 4}.…

A: c) we are given that the matrix M is  1110010000111001 which represents the relations R defined on…

Q: 14,497 where y is the 55000 and older with at least a indicates a linear relation nt of 0.7581.…

A: Note:As per the requirement of the students solving part(c). Let Y= a+bX be the regression line.…

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,…

Q: b) Let C = {1, 2, 3, 4}. Find a relation R on C that has exactly 3 ordered pair members and is both…

A: Given C = {1, 2, 3, 4}. We find a relation R on C that has exactly 3 ordered pair members and  both…