Write A here: A =. Let R be the relation on {0, 1, 2,3, 4, 5, 6, 7,8, 9} given by: (0,0), (0, 1), (0, 6), (1,0), (1,2), (1,5), (2,3), (2,8), |(3,2), (3,3), (3, 4), (3, 7), (4,0), (4, 5), (5,4), (5,5), (5,9), (6,2), (6,6), (6,7), (7,1), (7,6), (7,8), (8,4), (8, 9), (9,0), (9,3), (9,8) R:= a. Let S = (RN A²). Write out S below: S= b. Draw the directed graph of S.

Q: 10. What is the domain of the relation shown below? (1) {0, 1, 4} (2) {-2, –1, 0, 1, 2} {(4, 2).(1,…

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Q: Part (A): Recall that VA, B C U: (A = B): → (36 € Fnc(A,B)(Bij($))). Prove that (=) is an…

A: a) Given -∀A , B ⊆ μ : ( A ≃ B ) : ⇔∃ϕ ∈ Fnc(A,B)(Bij(ϕ)) To prove - ≃ is an equivalence relation on…

Q: 2. Which is the inverse of the relation {(-2,5), (-1,3), (0,-1), (1,-3), (2,-5), (3,-7)}? O {(5,-2),…

A: The given relation is -2,5,-1,3,0,-1,1,-3,2,-5,3,-7

Q: E. 1. Let R = {(0, 0), (1, 2), (2, 1), (2, 3), (3, 3)}be the relation on A = {0, 1, 2, 3}. Then, R2…

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Q: Let R be the relation {(1,2), (1,3), (2,3), (2,4), (3,1)} and let S be the relation {(2,1), (3,1),…

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Q: Let A = { 3, 9}, R relation on A defined R by. R = {(a, b): a +b = 12 ,a, b E A }. Write R. O a. {…

A: Given that A={3,9} R is a relation on A defined by R={(a,b):a+b=12,a,b belongs to A}

Q: 6. Find the transitive closure and the reflexive transitive closure of the relations R below defined…

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Q: 1. 2. b 1 1 0 1 3 0 1 1 0 0 0 1 1

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Q: Let A = {6, 9} , R relation on A defined R by. %3D R = {(a, b): a +2 = b -1 ,a, b E A}. Write R. %3D

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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: 2. The relations below are defined on the set {0,1,2,3}. Determine which of these relations are…

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Q: Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4,4),(1, 3),…

A: The given set and the relation R is shown below.

Q: 2. Identify which is a relation and a function. a. U = {(-1,1), (0, 1), (1,1), (2, 1), (3, 1)} b. W…

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

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Q: For each relation, decide whether or not that relation is reflexive, symmetric, antisymmetric or…

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Q: Let the relation S defined as S = {(x,y) | y = X2 + 4x +3}. What is the domain of S?

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Q: The inverse of a relation r is r {(0, 0), (0, 1), (0, 2) }. Which of the following may be the…

A: Topic = Relation   The Inverse of a Relation is a set of ordered pairs that is the exact inverse of…

Q: -1, -3, -5, –7}. Determine whether each relation on X is a fur (-3, –5), (–1, –7), (–3, –1), (–5,…

A: Introduction: A function is an expression, rule, or law in mathematics that defines a relationship…

Q: Let A={1,2,3,4}=B, Then write down the relation for P(x,y)=xZy where x,y E A

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Q: Let A = {1, 2, 4, 5, 6, 7, 8, 9} Let R be a relation on A defined by R = {(a, b) : a e A. b e A, a…

A: Given set is A=1,2,4,5,6,7,8,9 and R be the relation on A defined by R={(a,b):a∈A,b∈A,a is…

Q: 5. Let R be the relation on the set {1, 2, 3, 4, 5} containing the ordered pairs (1, 1), (1, 2), (1,…

A: Let R be the relation on the set 1 , 2 , 3 , 4 , 5 containing the ordered pairs  1 , 1 , 1 , 2 , 1 ,…

Q: Draw the shape of relation z - V3e Зе V3.

A: We are given the relation : z-3eiπ3=3---(1) Now, Let, z=x+iy---(2) Now, 3eiπ3=3cosπ3+i…

Q: Let X = {1, 2, 3, 4}. Let R = {(1, 3), (2, 1), (2, 2), (2, 3), (2, 4), (3, 3), (3, 4), (a, b) },…

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Q: B. Let A = (a, b. c. d). Let R be the relation on A defined as follows: R= {(a, a), (a, b), (a, c),…

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Q: Define a relation R2 on the set A = {0, 1, 2, 3} as follows.R2 = {(0, 0), (0, 1), (1, 1), (1, 2),…

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Q: Represent the relations on {1, 2, 3, 4} with a matrix and digraphs.  (The rows and columns…

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Q: Why

A: The given relation  R={(3,3),(4,4),(6,6),(7,7),(3,6),(6,3),(4,7),(7,4)}

Q: A// Which of these relations on {0, 1 , 2, 3 } are equivalence relations, why? a) R1= {(0, 0). (1 ,…

A: According to our guidelines we can answer only first question and rest can be reposted.

Q: Consider the relation on A = {a, b, c, d, e} given by R={(a,b),(b,c), (b,d),(b,e),(d,

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Q: Which is the inverse of the relation {(-2,5), (-1,3), (0,-1), (1,-3), (2,-5), (3,-7)}? O {(5.-2).…

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Q: 10. What is the domain of the relation shown below? {(4, 2),(1, 1).(0, 0),.(1, –1),(4, –2)} (3) {-2,…

A: Given relation is : 4,2,1,1,0,0,1,-1,4,-2 To find the domain of the given relation.

Q: Let X = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Let R1be a relation in X given by                  R1= {(x, y)…

A: Obtain the set R1 as follows.

Q: Let A={a,b,c,d} and let R={(a,b)(b,c)(c,d)(d,b)} be a relation on A. Represent the relation using…

A: Given  A = {a, b, c, d} R = { (a, b), (b, c), (c, d), (d, b)}

Q: Let A = { 1, 2, 3, 4 } and B = { 4, 6, 8, 10 }.Define a relation H from A x B as: For all (x, y) ∈ A…

A: Please see the below picture for detailed solution.

Q: Q3. Let R be the relation R (1, 2),(1, 3),(2, 3),(2, 4),(3, 1)} and S be the relation S= {(2, 1),…

A: Hence, if R be the relation   R={(1, 2),(1, 3),(2, 3),(2, 4),(3, 1)} and S be the relation S={(2,…

Q: Exercise 19. Let R be the relation given by the following digraph. Then (2)- a. (1.2.3) b. (1.3) c.…

A: Given - Let R be the relation given by the following digraph To find - Then 2 = ? 1, 2, 3 1, 3 3…

Q: E. 1. Let R= {(0, 0), (1, 2), (2, 1), (2, 3), (3, 3)}be the relation on A = {0, 1, 2, 3}. Then, R =…

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Q: Let A = (0,1,2,3). The relations R, S and T in the set A are defined as follows……

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Q: Let A = {#, 7, x} and let R be the relation on A given by R = {(7, 7), (#, #)}

A: R is  said to be reflexive relation on A if for all x in A, xRx holds.  R is said to be symmetric…

Q: 3. Let R be the relation defined by x R y + x² <y? Determine ifR is an order relation on N? on Z?…

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Q: cercise 2. Give an example of a relation R on A = {1,2,3} that is neither reflexive or irreflexive.

A: Given A = {1, 2, 3}

Q: Let A={5,10,15,20, 25} and a partition of A be: {5,25},{10, 20} , {15} (a) Write all pairs of the…

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Q: Let A = {1,2,3,4} and B = {A,B, C, D, E}. Consider the following relations and state whether…

A: A relation will be function if for each x∈A  there exists a unique b∈B with (a, b) ∈ f. In other…

Q: Consider the relation on A = {a, b, c, d, e} given by R={(a,b),(b,c),(b,d),(b,e),(d,e)}

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Q: Click and drag all relations on the set A= (0, 1) on the right column into the left column.…

A: Given : set A=0, 1 To find : all relations on set A Pre-requisite :  1. A relation on a set A is a…

Q: Let R be the relation {(1,2), (1,3), (2,3), (2,4), (3,1)} and let S be the relation {(2,1), (3,1),…

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

A: Given A=1,2,3,4 and B=x,y,z Let R be the following relation from A to B such that…

Q: Let X = {a,b,c} and Y = {1,2,3,4}. Which of the relations A,B,C defined below are functions from X…

A: The given problem is related with function. Given that ,               X = a , b , c and Y = 1 , 2 ,…

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…