Here you will learn what is equal function in maths with definitions and examples. Let’s begin – Equal Function in Maths Definition : Two functions f and g are said to be equal iff (i) domain of f = domain of g (ii) co-domain of f = codomain of g. and (iii) f(x) = g(x) …
Equal Function in Maths – Definition and Examples Read More »
Here you will learn what is equivalence relation on a set with definition and examples. Let’s begin – What is Equivalence Relation ? Definition : A relation R on a set A is said to be an equivalence relation on A iff it is (i) reflexive i.e. (a, a) \(\in\) R for all a \(\in\) …
What is Equivalence Relation – Definition and Examples Read More »
Here you will learn what is antisymmetric relation on sets with definition and examples. Let’s begin – What is Antisymmetric Relation ? Definition : Let A be any set. A relation R on set A is said to be an antisymmetric relation iff (a, b) \(\in\) R and (b, a) \(\in\) R \(\implies\) a = …
What is Antisymmetric Relation – Definition and Examples Read More »
Here you will learn what is transitive relation on set with definition and examples based on it. Let’s begin – What is Transitive Relation ? Definition : Let A be any set. A relation R on A is said to be a transitive relation iff (a, b) \(\in\) R and (b, c) \(\in\) R \(\implies\) …
What is Transitive Relation – Definition and Examples Read More »
Here you will learn what is symmetric relation on sets with definition and examples. Let’s begin – What is Symmetric Relation ? Definition : A relation R on a set A is said to be a symmetric relation iff (a, b) \(\in\) R \(\implies\) (b, a) \(\in\) R for all a, b \(\in\) A i.e. …
What is Symmetric Relation – Definition and Examples Read More »
Here you will learn what is reflexive relation on set with definition and examples. Let’s begin – What is Reflexive Relation ? Definition : A relation R on a set A is said to be reflexive if every element of A is related to itself. Thus, R is reflexive \(\iff\) (a, a) \(\in\) R for …
What is Reflexive Relation – Definition and Examples Read More »
Solution : Let A be a set. Then, the relation \(I_A\) = {(a, a) : a \(\in\) A} on A is called the identity relation on A. In other words, then the relation \(I_A\) on A is called the identity relation if every element of A is related to itself only. Example : If A …
Solution : Let A be a set. Then, A \(\times\) A \(\subseteq\) A \(\times\) A and so it is a relation on A. This relation is called the universal relation on A. In other words, a relation R on a set is called universal relation, if each element of A is related to every element …
Solution : Let A be a set. Then, \(\phi\) \(\subseteq\) A \(\times\) A and so it is a relation on A. This relation is called the void or empty relation on set A. In other words, a relation R on a set A is called void or empty relation, if no element of A is …
Here you will learn what is the complement of a set definition with venn diagram and examples. Let’s begin – Complement of a Set Definition : Let U be the universal set and let A be a set such that A \(\subset\) U. Then, the complement of A with respect to U is denoted by …
