A relation R on a set S is called a partial order if it satisfies three properties (one of which is new to us): I R is reflexive. II R is anti-symmetric: Vr, y E S, (xRy A yRx) = x = y. III R is transitive. Which of the following relations is a partial order on the set S = N? Select only one answer. (a) xRy = a² = y? (b) xRy + x|y (c) rRy + xy is even (d) xRy x + y is a prime number (e) xRy + xy > 3

Q: (2 1). If Let vi = 1 2 2 is ,V3 V4 3 a dependence relation on (v1, v2, V3, V4) thenx = a) 17 b) 15…

A: Here, we have v1=111, v2=123, v3=321, v4=210. If xy-1-3 is a dependence relation on v1, v2, v3, v4,…

Q: For the relation R closure of R. {(1,2), (1,4), (3,3), (4, 1)} find (i) R2 (ii) R3 and (iii)…

A: The given relation,

Q: 1. Consider the relation R = {(a, a),(b, b), (c, c), (d, d),(a, b), (b, a)} on set A = {a,b,c,d}. Is…

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Q: A group of 4 students namely Maiyra, Bansan, Kate and Davis from final semester in Computer Sciences…

A: (i) Let R be a relation defined by R=Maiyra, DIP, Bansan, Computer Vision, Kate, DIP, Davis, Pattern…

Q: (a) Let R be a relation on the set Z × Z defined by the following rule: For all (a, b),(c, d) ∈ Z ×…

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Q: 1. The following subsets A, B, and C of R XR are relations on R. Sketch the set. (i) B = {(x, y):…

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Q: A). C). X y y 7 - 2 - 2 - 1 - 1 - 4 4 - 5 1 1 -4 1 - 2 - 5 1 y 1 y B). D). - 2 - 2 - 1 6. 8. - 1 0.…

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Q: Draw the relation

A: Given: x,y/x2+y2≤1 To draw: The relation.

Q: Find, for each part of the question, an example of a set S and two relations R1 C S x S and R2 C S x…

A: Since the questions contains many subparts. As per the guidelines I am answering the first three…

Q: . A) Write the ordered pairs, graphical representation, and the relation matrix, for  the Relation R…

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Q: Suppose that R is the relation that is represented by the following digraph ... a O True O False b d…

A: The objective is to determine whether the directed graph with the relation is a partial order or…

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 > 0

Q: 1. Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Let P = P(A) be the power set of A. Let R be the relation on…

A: (a) For any X ∈ P,            | X ∪ X | = |X|           | X ∪ {1, 2} | = |X| + |{1, 2}| - |X ∩ {1,…

Q: If R and S are partial orders, then must ROS be a partial order? If not, explain why. Where is the…

A: Please see the below picture for detailed solution.

Q: 8. Which of the following relations is a partial order but not a linear order for A=(1,2,3}: *…

A: PARTIAL ORDER:                                                         ' A relation R is said to be…

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: 10) Let R be a relation on A = {1,2,3,4,5,6,7} as x R yx + y = 6. a. Find relative set R(B), where B…

A: (10) Consider the provide question,  (a)

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: 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: Let R be the relation on the set (0, 1, 2, 3} and R= {(0, 1), (1, 1), (1, 2), (2, 0), (2, 2), (3,…

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

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Q: 4), (4,2)} Draw the diagraph of R

A: # As per the guidelines we are entitled to solve three subparts at a time ,please resubmit the other…

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: Let A = {1, 2} and let B = {2, 4, 7}. Let R be a relation defined as follows: (x, y) = R means that…

A: Solution:

Q: prove why each relation has or does not have the properties: reflexive, symmetric, anti-symmetric,…

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Q: Let R and S be two relations both on A. Show that (a) If R and S are both reflexive, is RnS also…

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Q: Define the relation r on S = {A, B, C, D} by r ={ (A,B), A,D), (B,A), (B,C), (C,A), (C,B), (D,B)}.…

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Q: Let R and S be symmetric relations. Show: R ◦ S symmetric ⇔ R ◦ S = S ◦ R

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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: 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: 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: domain of a relation

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Q: Let A = {0, 1, 3, 4, 5, 6} and define the relation R and S on A as follows: For every (x, y ) eA,…

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