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: 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: Let A = {a, b, c} Define a relation as follows: ARA = {(a, b) , (a, c) , (b, c)} To obtain the…

A: Transitive relation means if (x, y) and (y, z) are in R, then (x, z) will also be in R.    Using…

Q: In a high school graduation class, (x,y) is in the relation r if person x is the same height as…

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Q: i Determine whether or not the relation R on the set of all real numbers is reflexive, symmetric,…

A: Note: We'll answer the first question since the exact one wasn't specified. Please submit a new…

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: Let R = {(x, y) ∣ x ≥ y} be a relation from set A = {6} to B = {5,7}. a. List the order pairs of…

A: Given,          R=x,y/x≥y          Set A=6          Set B=5,7

Q: Ppply the necessory for the given restrictions relation Ques tion 1 in order for it o be bi gec tive…

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Q: 3. Use finite differences to determine whether each relation is linear, quadratic, or neither. a) y…

A: To determine if the relation is linear, quadratic, or neither.

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: Let A — {1, 2, 3, 4} and B — {5, 6, 7}, and let f be the relation f = {(1, 5), (2, 5), (3, 6), y)}.…

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Q: Which of the following relations are transitive? The relations are in bold. (Remember: A relation R…

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Q: {(a, b) acb, a and b are finite set of integers}

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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 > 0

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: (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: 2 = y. Select the description that accurately describes The domain of a relation R is the set of…

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Q: (a) Consider the set A = {x² E Q1x ER}. Determine whether A is closed under addition and…

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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: What is the point of a partial order? a. We would like to generalize the properties of the relation…

A: Numbers are easily comparable. But two elements may satisfy either of the relations, a=b, a&lt;b,…

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: 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: i). Find the highest normal form of a relation R(A,B,C,D,E) with FD set as (BC->D, AC->BE, B->E}

A: As we can see, (AC)+ = {A, C, B, E, D} but none of its subset can determine all attribute of…

Q: The domain of a relation R is the set of integers. x is related to y under relation R if x 2 = y.…

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Q: Consider the recurrent relation: An = An-1 + 4 n2 0, A1 = 0 %3D a. The given definition is correct…

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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…

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

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Q: Consider a relation R on the set A = {1, 2, 3, 4} defined by R = {(1, 2), (2, 3), (3, 4), (4, 1)}.…

A: A relation R on a set A is said to be:Reflexive: If every element of set A is related to itself.…

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: List the ordered pairs in the relation R from A={0,1,2,3,4} to B={0,1,2,3} where (x,y) R if only if…

A: 1. As 0≤0, 0≤1, 0≤2, 0≤3, 1≤1, 1≤2, 1≤3, 2≤2, 2≤3, 3≤3 So the ordered pairs relation is R = {(0, 0),…

Q: Recall that a prime number is an integer that is greater than I and has no positive integer divisors…

A: We will use explanation when  the relation satisfies and will use counter example when it does not .…