Class 12 Math Chapter 1 Relation & Functions Notes PDF (Handwritten Notes PDF)

Some students find Math a very hard subject so here on BoardStudy, we have shared class 12 Math Chapter 1 Relation & Functions notes PDF. We have covered every topic in a simple and easy way so anyone can understand the chapter and perform well in exam.

Notes are very clean and colourful written by BoardStudy subject matter experts. Every important concept, formula, diagram and derivation is shared in Relation & Functions notes that will help you solve the problem. These notes are designed to make complex topics easier which will definitely boost the students’ confidence during the exam.

Relation & Functions Handwritten Notes PDF

Also check: Class 12 Biology Notes PDF

Key Points: Relation & Functions Notes

Relation

• A relation is a set A is a subset of A x A
• In other words elements of set A are related to itself if there is a relation in set A.

Types of relation

• Universal relation: If R=A x A or R=A x B then R is universal relation.
• Identity relation:
• Equivalence relation: A relation R defined on a set A is said to be equivalence relation if R is reflexive, symmetric and transitive.
• Reflexive relation

Equivalence classes:

• For an arbitrary equivalence relation R in an arbitrary set X, R divides X into two mutually disjoint subsets A₁, A₂ etc called partitions or sub-divisions of X satisfying:

Function

• Let X and Y be two non-empty sets. A function or mapping f from X into Y written as f: X→ Y is a rule by which each element x ∈ X is associated to a unique element y ∈ Y. Then f is said to be a function from X to Y.
• The elements of X are called domain of f.
• The elements of Y are called codomain of f.

Types of function

• One-one or Injective
• Many one function
• Onto or Surjective function
• Into function
• Bijective or one-one & onto function
• Bijective or one-one & onto function

Features of Notes

• Relation & Functions Notes are crafted by BoardStudy expert. All concept and diagram are included in notes.
• Our revision notes makes complex topic very simpler. By using our notes students can quickly revise Relation & Functions chapter.
• In the last few days of exam students feel very stress due to pressure of exam. Relation & Functions Notes will be very helpful for managing the stress in the last days of exam.

Summary