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    Types of Relation 1

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    Justin Adrian Bautista
    This document defines and provides examples of different types of relations: empty relation, universal relation, identity relation, inverse relation, reflexive relation, symmetric relation, transitive relation, and equivalence relation. An empty relation contains no ordered pairs, a universal relation contains all possible ordered pairs, and an identity relation contains ordered pairs that match elements to themselves. Inverse, reflexive, symmetric, and transitive relations have specific properties regarding how elements are related. An equivalence relation is reflexive, symmetric, and transitive. Examples are provided to illustrate each type of relation.

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    Types of Relation 1

    Uploaded by

    Justin Adrian Bautista
    41 views17 pages
    This document defines and provides examples of different types of relations: empty relation, universal relation, identity relation, inverse relation, reflexive relation, symmetric relation, transitive relation, and equivalence relation. An empty relation contains no ordered pairs, a universal relation contains all possible ordered pairs, and an identity relation contains ordered pairs that match elements to themselves. Inverse, reflexive, symmetric, and transitive relations have specific properties regarding how elements are related. An equivalence relation is reflexive, symmetric, and transitive. Examples are provided to illustrate each type of relation.

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    Types of Relation 1 (1)

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    This document defines and provides examples of different types of relations: empty relation, universal relation, identity relation, inverse relation, reflexive relation, symmetric relation, transitive relation, and equivalence relation. An empty relation contains no ordered pairs, a universal relation contains all possible ordered pairs, and an identity relation contains ordered pairs that match elements to themselves. Inverse, reflexive, symmetric, and transitive relations have specific properties regarding how elements are related. An equivalence relation is reflexive, symmetric, and transitive. Examples are provided to illustrate each type of relation.

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    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    41 views17 pages

    Types of Relation 1

    Uploaded by

    Justin Adrian Bautista
    This document defines and provides examples of different types of relations: empty relation, universal relation, identity relation, inverse relation, reflexive relation, symmetric relation, transitive relation, and equivalence relation. An empty relation contains no ordered pairs, a universal relation contains all possible ordered pairs, and an identity relation contains ordered pairs that match elements to themselves. Inverse, reflexive, symmetric, and transitive relations have specific properties regarding how elements are related. An equivalence relation is reflexive, symmetric, and transitive. Examples are provided to illustrate each type of relation.

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    of 17

    TYPES OF

    RELATION
    By Group 7
    I. Relation
    II. Types Of Relation
    - Empty Relation
    Table of - Universal Relation
    - Identity Relation

    Content - Inverse Relation


    - Reflexive Relation
    - Transitive Relation
    - Equivalence Relation
    RELATION
    A relation is a relationship
    between sets of values. In
    math, the relation is between
    the x-values and y-values of
    ordered pairs
    EMPTY RELATION
    A void relation in which there is
    no relation between any elements
    of a set.
    If there is a relation R EXAMPLE
    on Set A is called an
    empty relation. if no A = {1, 2, 3}
    element of A is related R = {(a, b ∈ A, a + B = 10}
    to any other element of
    A. A x A = ({1,1), (1,2),
    (1,3), (2,1), (2,2), (2,3),
    R=φ⊂A×A (3.1), (3.2), (3,3)}.
    INVERSE RELATION
    a set has elements in which are
    inverse pairs of another set. Let R
    be a relation from set A to set B R
    ∈ A x B.
    The relation R-1 is said Example
    to be an inverse
    Relation if R-1 from Set
    B to A is denoted by R-1 (1, 3), (1, 2), (5, 7)
    = {(b, a): (a,b) ∈R}. \ /
    (3, 1), (2, 1), (7, 5)
    R-1 = {(b, a): (a, b) ∈ R}
    REFLEXIVE RELATION
    relation is the one in which
    every element maps to itself.
    Example

    set A = {1, 2}

    R = {(1, 1), (2, 2), (1, 2), (2, 1)}.

    (a, a) ∈ R ∀ a ∈
    A
    SYMMETRIC RELATION
    A relation R on a set A between two or more elements
    is said to be of a set is such that if the first
    symmetric if (a, b) ∈ element is related to the
    R then (b, a) ∈ R, for second element.
    all a & b ∈ A..
    Example Example

    R = {(1,1), (2, 2), (3, 3)}

    A = {1, 2, 3}
    TRANSITIVE RELATION
    Transitive relations are binary
    relation in set theory that are
    defined on a set A such that if a
    is related to b and b is related to
    c, then element a must be
    related to element c, for a, b, c in
    set A.
    Example Example

    Let A = { 1, 2, 3 }

    R = {(1, 2), (2, 3), (1, 3)}


    EQUIVALANCE RELATION
    A relation is said to be equivalence
    if and only if it is Reflexive,
    Symmetric, and Transitive.

    Equivalence relations are often


    used to group together objects
    that are similar, or “equiv- alent”,
    in some sense.
    Example

    R= {(a, b): a ∈ A, b ∈ B} {(1, 1), (2, 2), …, (6, 6) ∈ R}

    {(a, b) = (1, 2) ∈ R} {(b, a) = (2, 1) ∈ R}

    {(a, b) = (1, 2) ∈ R} {(b, c) = (2, 3) ∈ R}

    {(a, c) = (1, 3) ∈ R}
    That’s All Thank you!
    MEMBER

    MARTINEZ
    MAULA
    JAENA
    LOSIGRO

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