In the set of animals, a relation R is defined in each question. On the set of human beings a re

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In the set of animals, a relation R is defined in each...

In the set of animals, a relation $\mathrm{R}$ is defined in each question. On the set of human beings a relation $\mathrm{R}$ is defined as follows: $a \mathrm{R} \mathrm{b}$ if $^{\prime \prime} \mathrm{a}$ and $\mathrm{b}$ have the same brother", then $\mathrm{R}$ is (1) only reflexive (2) only symmetric (3) only transitive (4) equivalence

In the set of animals, a relation $\mathrm{R}$ is defined in each question.
On the set of human beings a relation $\mathrm{R}$ is defined as follows:
$a \mathrm{R} \mathrm{b}$ if $^{\prime \prime} \mathrm{a}$ and $\mathrm{b}$ have the same brother", then $\mathrm{R}$ is
(1) only reflexive
(2) only symmetric
(3) only transitive
(4) equivalence

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Key Concepts

Equivalence Relation

An equivalence relation is a specific type of binary relation that is reflexive, symmetric, and transitive. Equivalence relations are important because they partition a set into distinct equivalence classes, grouping elements that are considered equivalent under the relation.

Transitivity

Transitivity is a property that holds for a relation if whenever an element a is related to b and b is related to c, then a must also be related to c. This property allows the relation to extend over sequences of connected elements.

Reflexivity

Reflexivity is a property of a relation where every element in the set is related to itself. In other words, for every element a, the relation must include the pair (a, a).

Binary Relation

A binary relation is a mathematical concept that links elements of a set in ordered pairs, providing a framework to discuss relationships between these elements. It forms the basis for exploring various relational properties in different contexts.

Symmetry

Symmetry in a relation means that if an element a is related to an element b, then b is also related to a. This mutual relationship is critical in understanding how pairs interact within the larger set.

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