The relation p = ((a, b) e R x R: 1+ ab > 0} is %3D (a) reflexive, symmetric but not transitive. (b) an equivalence. (c) transitive, symmetric but not reflexive. (d) reflexive, transitive but not symmetric.

Q: 11. ( a) b) c) ) Consider the relation on A={1,2,3) represented by the matrix Determine if the…

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Q: b) Let X = (x, y, z). Then show that A = {(x,x),(y,y),(z,z)} is an equivalence relation. Determine…

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Q: Let R1 = {(a,b) E R²|a > b}, R2 = {(a, b) E R²|a < b} and a) R3 = {(a, b) E R²|a + b} be relations…

A: we have  R1={(a,b)∈R2|a≥b}R2={(a,b)∈R2|a&lt;b}R3={(a,b)∈R2|a≠b}

Q: Consider the relation R on R, where R = {(a, b) | ab ≥ 0} . (a) Is the relation R reflexive,…

A: is a relation on

Q: 1. Let A = {blue, yellow, red}, B = of the relations below (a) determine if it is a function (b) if…

A: R1: D X B={(cat,blue),(cat,red)} So, {(cat,blue)} ⊂{(cat,blue),(cat,red)} Therefore R1 is a…

Q: What is the reflexive closure of the relation R = {(a, b) | a > b} on the set of integers? Select…

A: Reflexive Relation Definition:  A reflexive relation is the one in which every element maps to…

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: Determine whether the relation R is a partial order relation on the set of positive…

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Q: 2. Let A:= {1,2, 3, 4} =: B and T:= {(a, b) E A x B | l e Z}. (a) Find A x B. (b) Find T (c) Check…

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Q: D(x): x can drive F(X): x is in my family The universe of discourse consists of everybody in my…

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Q: (2.3) Prove that R is an equivalence relation.

A: Prove R is an equivalnce relation.

Q: ii. Determine whether the relation, R = {(1, 3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)} is: Yes/No…

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Q: Compute the complement of relation R. R={(1, 1), (5, 1), (5, 5), (6, 1), (6, 6), (7, 1), (7, 7)}

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Q: Determine if the relation R = {(1,3), (1,4), (2,3), (2,4), (3,4)} is reflexive, symmetric,…

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Q: consider the relation R={(1,a),(1,b), (3,b),(3,d), (4,b)} form X={1,2,3,4} and Y={a,b,c,d}. Thus…

A: Consider the relation

Q: Consider the relation R = {(a, a), (c, a), (b, c), (d, b)} then which of the following set…

A: We need to find R3 given R=a,a,c,a,b,c,d,b Now,  R2=RοRR3=RοR2=R2οR The composition of two…

Q: Determine whether the relation R on A is an equivalence relation and provide your reasoning: а.…

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Q: Let R₁ and R₂ both be equivalence relations. Show by proof or disprove by counterex- ample the…

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Q: Let A = {0, 1, 2, 3), and dene a relation R on A as follows: R = {(0, 2), (0, 3), (2, 0), (2, 1) }…

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Q: The function f(x) = -X-3)2 - 4, will have a shift of 4 units to the left. O True O False

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Q: Define a relation R on Z as follows: For all integers m and n, 51(m² - n²). mRn (a) Is 1 R (-4)? Yes…

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Q: Find the closed form of the relations: Note the index! an = do = = 13 an = 5an-1 +8

A: Detailed explanation:Given:             a0​​=13            an​​=5an−1​​+8 Step 1: Solve the…

Q: C = {4x + 1] x € Z+}, D = {c + d]c € C, d € C}, E = C × D Is C a subset of D or E? Explain a…

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Q: 4. Let R be the relation xRy if 3| (x – y) on Z. Prove that R is an equivalence relation.

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Q: (c) The reversed relation R is an equivalence relation. (d) So R is an equivalence relation if and…

A: (c) If R is an equivalence relation in a set X, then it is reflexive, symmetric and transitive.

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

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Q: 4. Let the relation R = { (a, b) e Z × Z l(a + b) = 1 (mod 5) }. a. Is the relation transitive?…

A: A relation R between two sets A and B is the set of all ordered pairs a,b such that a∈A and b∈B. We…

Q: Define the relation R over integers as follows: R = { (a, b) | |a - b| < 5 } Determine if R is (a)…

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Q: 11. ( a) b) c) [1 1 1 ) Consider the relation on A={1,2,3) represented by the matrix 0 10 0 1 1…

A: 11. Consider the relation on A = {1, 2, 3} represented by the matrix 111010011   (a) To determine:…

Q: Prove or disprove: If a relation is symmetric and transitive, then it is also reflexive

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Q: Let A={1,2,3,4,5,6} and consider the following 3 subsets of A. A, = {1,3,5}; Az : %3D %3D %3D {2,4,…

A: Let A=1,2,3,4,5,6 and 3 subsets of A. A1=1,3,5; A2=2,4,6,A3=3,6 we have a relation xRy if and only…