Key Notes
Chapter-01
Relation and Function
TYPES OF RELATIONS:
• A relation R in a set A is called reflexive if (a, a) ∈ R for every a ∈ A.
• A relation R in a set A is called symmetric if (a1, a2) ∈ R implies that (a2, a1) ∈ R, for all a1,
a2 ∈
• A relation R in a set A is called transitive if (a1, a2) ∈ R, and (a2, a3) ∈ R together imply
that (a1
• all a1, a2, a3 ∈ A.
EQUIVALENCE RELATION
• A relation R in a set A is said to be an equivalence relation if R is reflexive, symmetric and
transitive.
Equivalence Classes
• Every arbitrary equivalence relation R in a set X divides X into mutually disjoint subsets
(Ai) called partitions or subdivisions of X satisfying the following conditions:
• All elements of Ai are related to each other for all i
• No element of Ai is related to any element of Aj whenever i ≠ j
• Ai ∪ Ai = X and Ai ∩ Ai = Φ , i ≠ j . These subsets ( (A i ) ) are called equivalence classes.
• For an equivalence relation in a set X, the equivalence class containing a ∈ X, denoted by
[a], is the subset of X containing all elements b related to a.
**Function: Arelation f: A
→ B is said to be a function if every clement of A is
correlated to a
Unique element in B.
*Aisdomain
* Biscodomain
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Portal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks
Chapter-01
Relation and Function
TYPES OF RELATIONS:
• A relation R in a set A is called reflexive if (a, a) ∈ R for every a ∈ A.
• A relation R in a set A is called symmetric if (a1, a2) ∈ R implies that (a2, a1) ∈ R, for all a1,
a2 ∈
• A relation R in a set A is called transitive if (a1, a2) ∈ R, and (a2, a3) ∈ R together imply
that (a1
• all a1, a2, a3 ∈ A.
EQUIVALENCE RELATION
• A relation R in a set A is said to be an equivalence relation if R is reflexive, symmetric and
transitive.
Equivalence Classes
• Every arbitrary equivalence relation R in a set X divides X into mutually disjoint subsets
(Ai) called partitions or subdivisions of X satisfying the following conditions:
• All elements of Ai are related to each other for all i
• No element of Ai is related to any element of Aj whenever i ≠ j
• Ai ∪ Ai = X and Ai ∩ Ai = Φ , i ≠ j . These subsets ( (A i ) ) are called equivalence classes.
• For an equivalence relation in a set X, the equivalence class containing a ∈ X, denoted by
[a], is the subset of X containing all elements b related to a.
**Function: Arelation f: A
→ B is said to be a function if every clement of A is
correlated to a
Unique element in B.
*Aisdomain
* Biscodomain
Material downloaded from http://ncrtsolutions.in and http://ncrtsolutions.in
Portal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks
