Let ≥ be a relation defined on sets A and B by A ≥ B iff there exists a surjective function f : A → B. Show that ≥ is not an equivalence relation.

Q: If A = {1,2,3,4} give an example of a relation R on A that is: Reflexive and symmetric but not…

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Q: 35. For each real number x, let f(x)=x². For any two real numbers a and b, define a -b provided that…

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Q: Determine if the relation ? = {(f, g)|f(x) = g(x) for some x ∈ ℝ} on the set of all functions from ℝ…

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Q: Let S be the set of all real numbers and let R be a relation in S, defined by R = {(a, b): a < b?.…

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Q: Let A be the set of all students of a boys school. Show that the relation Rin A given by R = {(a, b)…

A: It is given that, A is the set of all students of a boys school.Show that R is an empty…

Q: Let A = {x, y, z}. Write down a relation R on A that is not reflexive, not sym- metric, and 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 and B be two nonempty sets, f: A → B be a function and R be an equivalence relation on the set…

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Q: Given a relation g from the set D = {1, 2, 3, 4, 5} to the set C = {a, b, c, d}, where g = {(1, a),…

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Q: 2. Let R = {(x, y) = R x R = |x] + [y] =4}. Then R is a relation on R. Is R an equivalence relation…

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Q: 2) Define a relation R from {a, b, c} to {u, v} as follows: R = {(a, v),(b, u),(b, v),(c, u)}. a)…

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Q: Let A = {3,4,5,6} and B = {1,2,3} and define a relation R: A → B as follows: For all (x, y) ∈ A × B,…

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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 F be a nonempty family of transitive relations. Prove that intersection F is a transitive…

A: Given F be a nonempty family of transitive relations. We have to prove that the intersection F is a…

Q: A = Z*; a R b if and only if |a – b| < 2.

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Q: 9. Let R+ denote the set of positive real numbers. Define a relation E on R+ as follows: a Eb if and…

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Q: On sets, the relation x R y given by there exists a bijective function from the set x to the set y'…

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Q: A = {1, 3} and B = {2, 4, 6}. Define a relation R from A to B as follows: for all (x, y) ∈ A × B…

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Q: Let R be a reflexive relation on A. Show that R" is reflexive for all positive integers n.

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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: 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: set {(a,b),(a, a), (c, a), (b, b)} (a). Let X = {a,b,c} be sets. is a relation on X and find its…

A: Answer and explanation is given below..

Q: Decide whether each of the following relations is an equivalence relation or not.  {(a, b) | gpa of…

A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…

Q: Let R be a relation on Z given by aRb if and only if a = b². Is this relation a function? Justify…

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Q: Let R be a relation defined on Z as follows: (a,b) is an element of R if and only if the square of a…

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Q: Let R be the relation on a set A = {a, b, c, d} defined by R= {(a, a), (a, b), (b, b), (b, c), (c,…

A: If R is a relation on a set A, then R^2 is the set of ordered pairs (a, c) such that there exists an…

Q: Let f : X → Y be a function. Define a relation R in X given byR = {(a, b): f(a) = f(b)}. Examine…

A: Given:

Q: To find an equivalence class of x ϵ X determined by the relation R ⊆ X ⨯ X, R must be an equivalence…

A: Equivalence Relation: A relation R in X is called an equivalence relation if it is reflexive,…

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: Define a relation R on the x-y plane as follows: Given two points (x1 ,y1) and (x2 ,y2) in the x-y…

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Q: Let R be the relation on a set A = {a, b, c, d} defined by R = {(a, a), (a, b), (b, b), (b, c), (c,…

A: The given relation  on a set  is defined as follows..We need to find .

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: A relation on a set A is circular iff , y, z x~y and y~z implies z~x. Prove that a relation is an…

A: The relation on a set is a subset of the Cartesian product of the set. Therefore, each element is in…