Let f : R → R with f(x) = |5x−3|. Prove or disprove that f is injective (one-to-one).

Q: Let R be a relation that is symmetric and antisymmetric. Show that R is transitive

A: Let R be the relation which is symmetric and Anti-symmetric.We will show that R is transitive, that…

Q: ) Let R = {(a,b) : 3keza = k * b} be a relation over the positive integers. Prove or disprove that R…

A: Given that R=(a,b):a=k*b To show reflexive it is enough to show that a~a. It is true because, a=1*a.…

Q: 1. Give an example of a set S with a relation ~ on S such that ~ is symmetric and transitive but not…

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

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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: Draw the directed graph of the relation R on A = {1,2,3,4,5,6,7,8} defined as R = {(a,b)|a,b e A and…

A: Here, the relation is: R=(a,b)|a,b∈A and a≡b mod 3 That is: a-b is divisible by 3. So, 7-1=6 is…

Q: 1. Determine whether R = {(x, y) | x + y = 0} on the set of all real numbers is reflexive,…

A: Since you have posted a multiple question according to guildlines I will solve first(Q1) question…

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: Let R be a relation on the set A = {x € Z:1 < x < 100} defined as follows: x R y if and only if x-y…

A: Equivalence relation

Q: Let A ={1, 2}, B = {1, 2, 3} define a relation R from A to B given any {x, y} ϵ A cross B.…

A: A=1, 2, B=1, 2, 3 R is a relation defined as R=x, y: x+y2 is an integer.

Q: #14

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Q: 8. Define a relation on Z as xRy if |x-y| < 1. Is R reflexive? Symmetric? Transitive? If a property…

A: Given, Define a relation on Z as xR y if |x-y| &lt; 1. we have to find Is R reflexive? Symmetric?…

Q: Let A = {6, 8, 13, 15, 9, 16} and define a relation R on A as follows: xRy ⟺ 7 |(x – y) Draw a…

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Q: Let A = {0, 1, 3, 5, 7, 8} and R be a relation defined on A such that R= {(x , y)| 4 divdes (x –…

A: We are given the set A = {0, 1, 3, 5, 7, 8} and the relation R defined on A such that R = {(x, y)| 4…

Q: 6. Let R be the following relation on {a, b, c, d, e}. MR = (ants) Represent R with a digraph. TULLE…

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Q: 1. Define a relation R on R? by stating that (a, b)R(c, d) if and only if a? + b <c? +d². Show that…

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Q: (a) x and y are in the same major. (b) x and y have the same last name. (c) x and y are taking a…

A: See the attachment

Q: r1 1 1 0- 1 0 0 c) The matrix M represents the relations R defined. = 1 1 11 the set A = {1, 2, 3,…

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Q: Define the relation R on Z as follows: for x, y ∈ Z, xRy if and only y−x ≥ 0. Determine whether R is…

A: partial order means reflexive and antisymmetric.

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

A: Since you have posted multipart question and we can answer three subparts. So, answering the first…

Q: Let A = {1, 2, 3, 4, 5} and R be a relation on A such that for all x and y in A, x R y if and only…

A: Given data A={1,2,3,4,5}

Q: The following definitions are used: a relation on a set A is defined to be irreflexive it, and only…

A: The given set is A=01,2,3 The given relation is R=0,0,0,1,0,2,1,2. (i) Using the definitions of…

Q: 4. Define a relation R on N by aRb if a and b have no common factors except 1. (a) Give an example…

A: We have define  a relation R on natural numbers (N) by aRb if a and b have no common  factors except…

Q: 1. Let R be the relation on N defined by "aRb if EN or 5| (b- a)". So for example (6, 2) € R and…

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Q: 5. Let X be the set X = {1,2,3}, and let R be the relation defined on X by x₁ Rx₂ if x1 + x2 3. (a)…

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Q: Reflexive. • Anti-reflexive. • Symmetric. • Anti-symmetric. Justify all your answers. Transitive. •…

A: Let's consider a few examples of elements inside the relation R, where (a,b)∈ R if and only if…

Q: (b) Let {A₁, A2,...} be a partition of a set X, and R the relation {(x, y) = X²: there exists j such…

A: An equivalence relation is a binary relation between two elements of a set that satisfies three…

Q: Let A = {0, 1, 2, 3), and define a relation R, on A as follows: R₂ = (0, 0), (0, 1), (1, 1), (1, 2),…

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Q: Let A = {1, 2, 4, 5, 6, 10} and R be a relation on A such that for all x and y in A, x R y if and…

A: Given : A = {1,2,4,5,6,10} xRy if and only if x|y

Q: Let R be a relation from X to Y and S be its reverse relation from Y to X. Prove or disprove that R…

A: According to the given information it is required to prove/disprove that R is injective and well…

Q: Let R be a relation from A to B and S a relation from B to A. Prove or disprove that if S of R =…

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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: 1. Let A = {2, 3, 4, 5, 6} and B = {10, 11, 12, 13). Define a relation R on (A x B) as follows: a Rb…

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Q: . Define a relation R on Z as follows: a Rb if and only if 5 | (a²- 6²). Find four integers which…

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Q: Let R be a relation from A to B and S a relation from B to A. Prove or disprove that if S of R =…

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Q: 1. Let A = {cat,dog,bird,rat} and R be a relation on A defined by {(x,y) : x and y have at least one…

A: We have to solve given problem:

Q: 1. if R and T are anti-symmetric relations on a set A then (R U T) is anti-symmetric relation on А.

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Q: 4. Consider a relation R on X={a,b,c}. R= {(a,a), (b,b), (b,c), (c,b)} Please determine whether R is…

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