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An equivalence relation on a set is one that is transitive, reflexive and symmetric. Given a set A with n elements, the largest equivalence relation is AXA since it has n2 elements. Given any element a of the set, the smallest equivalence relation is (a,a) which has n elements.
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What do you mean by equivalence relation Give atleast two examples of equivalence relation?
An relation is equivalent if and only if it is symmetric, reflexive and transitive. That is, if a ~ b and b ~a, if a ~ a, and if a ~ b, and b ~ c, then a ~ c.
What is an equivalent?
Could you be more specific? An equivalence relation effectively partitions a set into nonoverlapping subsets.
What is an equivalence modulo?
An equivalence modulo is a relation between elements of a set, where two elements are considered equivalent if they have the same remainder when divided by a fixed number called the modulus. For example, in modulo 5 arithmetic, the equivalence class of 2 would include all numbers that leave a remainder of 2 when divided by 5: {2, 7, 12, 17, ...}. Equivalence modulo is often used in number theory and modular arithmetic.
If S equals straight lines in the plane and ab if a and b are parallel Verify that the relation is an equivalence relation on the set S given?
Establishing equivalence depends on the definition of parallel lines. If they are defined as lines which cannot ever meet (have no point in common), then the relation is not reflexive and so cannot be an equivalence relation.However, if the lines are in a coordinate plane and parallel lines are defined as those which have the same gradient then:the gradient of a is the gradient of a so the relationship is reflexive ie a ~ a.if the gradient of a is m then b is parallel to a if gradient of b = m and, if the gradient of b is m then b is parallel to a. Thus the relation ship is symmetric ie a ~ b b ~ a.If the gradient of a is m then b is parallel to a if and only if gradient of b = gradient of a, which is m. Also c is parallel to b if and only if gradient of c = gradient of b which is m. Therefore c is parallel to a. Thus the relation is transitive, that is a ~ b and b ~ c => a ~ c.The relation is reflexive, symmetric and transitive and therefore it is an equivalence relationship.
How many equivalence relations are there on a set with four elements?
16
What is Equivalence class?
An equivalence relation ~ on A partitions into pairwise disjoint subsets called equivalence classes so that 1. Within each class, every pair relates 2. Between classes there is no relation i.e. [x] = {a (element) A | a~x} and given two equivalence classes [a] and [b], either [a] = [b] or [a] intersect [b] = the empty set
What do you mean by equivalence relation Give atleast two examples of equivalence relation?
An relation is equivalent if and only if it is symmetric, reflexive and transitive. That is, if a ~ b and b ~a, if a ~ a, and if a ~ b, and b ~ c, then a ~ c.
What is meant by symmetric reflexive and transitive property and also equivalence relation?
First, let's define an equivalence relation. An equivalence relation R is a collection of elements with a binary relation that satisfies this property:Reflexivity: ∀a ∈ R, a ~ aSymmetry: ∀a, b ∈ R, if a ~ b, then b ~ aTransitivity: ∀a, b, c ∈ R, if a ~ b and b ~ c, then a ~ c.
What is an equivalent?
Could you be more specific? An equivalence relation effectively partitions a set into nonoverlapping subsets.
What is an equivalence modulo?
An equivalence modulo is a relation between elements of a set, where two elements are considered equivalent if they have the same remainder when divided by a fixed number called the modulus. For example, in modulo 5 arithmetic, the equivalence class of 2 would include all numbers that leave a remainder of 2 when divided by 5: {2, 7, 12, 17, ...}. Equivalence modulo is often used in number theory and modular arithmetic.
What are equivalence relations?
An equivalence relation r on a set U is a relation that is symmetric (A r Bimplies B r A), reflexive (Ar A) and transitive (A rB and B r C implies Ar C). If these three properties are true for all elements A, B, and C in U, then r is a equivalence relation on U.For example, let U be the set of people that live in exactly 1 house. Let r be the relation on Usuch that A r B means that persons A and B live in the same house. Then ris symmetric since if A lives in the same house as B, then B lives in the same house as A. It is reflexive since A lives in the same house as him or herself. It is transitive, since if A lives in the same house as B, and B lives in the same house as C, then Alives in the same house as C. So among people who live in exactly one house, living together is an equivalence relation.The most well known equivalence relation is the familiar "equals" relationship.
What is the relation between pK and pH?
At half equivalence (half neutralisation) pH=pK.
How many equivalence relations are there on a set with four elements?
16
If S equals straight lines in the plane and ab if a and b are parallel Verify that the relation is an equivalence relation on the set S given?
Establishing equivalence depends on the definition of parallel lines. If they are defined as lines which cannot ever meet (have no point in common), then the relation is not reflexive and so cannot be an equivalence relation.However, if the lines are in a coordinate plane and parallel lines are defined as those which have the same gradient then:the gradient of a is the gradient of a so the relationship is reflexive ie a ~ a.if the gradient of a is m then b is parallel to a if gradient of b = m and, if the gradient of b is m then b is parallel to a. Thus the relation ship is symmetric ie a ~ b b ~ a.If the gradient of a is m then b is parallel to a if and only if gradient of b = gradient of a, which is m. Also c is parallel to b if and only if gradient of c = gradient of b which is m. Therefore c is parallel to a. Thus the relation is transitive, that is a ~ b and b ~ c => a ~ c.The relation is reflexive, symmetric and transitive and therefore it is an equivalence relationship.
What is the domain of a relation?
It is the set on which the relation is defined to the set which is known as the range.
If a set of ordered pairs is not a relation can the set still be a function?
If a set of ordered pairs is not a relation, the set can still be a function.
What is The relation is the set of output values for the relation?
A relation doesn't have an "output value", in the sense that a function does. A set of values is either part of the relation, or it isn't.
