## Relations and Functions Maths Formulas for Class 12 Chapter 1

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- Empty relation holds a specific relation R in X as:
**R = φ ⊂ X × X**. - A Symmetric relation R in X satisfies a certain relation as:
**(a, b) ∈ R****implies (b, a) ∈ R**. - A Reflexive relation R in X can be given as:
**(a, a) ∈ R; for all ∀ a ∈ X**. - A Transitive relation R in X can be given as:
**(a, b) ∈ R and (b, c) ∈ R, thereby, implying (a, c) ∈ R**. - A Universal relation is the relation R in X can be given by R = X × X.
- Equivalence relation R in X is a relation that shows all the reflexive, symmetric and transitive relations.

*Properties*

- A function f: X → Y is one-one/injective; if f(x
_{1}) = f(x_{2}) ⇒ x_{1}= x_{2}∀ x_{1}, x_{2}∈ X. - A function f: X → Y is onto/surjective; if given any y ∈ Y, ∃ x ∈ X such that f(x) = y.
- A function f: X → Y is one-one and onto or bijective; if f follows both the one-one and onto properties.
- A function f: X → Y is invertible if ∃ g: Y → X such that gof = I
_{X}and fog = I_{Y}. This can happen only if f is one-one and onto. - A binary operation \(\ast\) performed on a set A is a function \(\ast\) from A × A to A.
- An element e ∈ X possess the identity element for binary operation \(\ast\) : X × X → X, if a \(\ast\) e = a = e \(\ast\) a; ∀ a ∈ X.
- An element a ∈ X shows the invertible property for binary operation \(\ast\) : X × X → X, if there exists b ∈ X such that a \(\ast\) b = e = b \(\ast\) a where e is said to be the identity for the binary operation \(\ast\). The element b is called the inverse of a and is denoted by a
^{–1}. - An operation \(\ast\) on X is said to be commutative if a \(\ast\) b = b \(\ast\) a; ∀ a, b in X.
- An operation \(\ast\) on X is said to associative if (a \(\ast\) b) \(\ast\) c = a \(\ast\) (b \(\ast\) c); ∀ a, b, c in X.

#### Summary of Relations and Functions formulas

We have listed top important formulas for Relations and Functions for class 12 Chapter 1 which helps support to solve questions related to chapter Relations and Functions. I would like to say that after remembering the Relations and Functions formulas you can start the questions and answers solution of the Relations and Functions chapter. If you faced any problem to find the solution of Relations and Functions questions, please let me know through commenting or mail.

### Maths Formulas for Class 12 by Chapters

Here Check Maths formulas for class 12 by chapter wise.

- Chapter 1 Relations and Functions
- Chapter 2 Inverse Trigonometric Functions
- Chapter 3 Matrices
- Chapter 4 Determinants
- Chapter 5 Continuity and Differentiability
- Chapter 7 Integrals
- Chapter 8 Applications of Integrals
- Chapter 10 Vector Algebra
- Chapter 11 Three dimensional Geometry
- Chapter 13 Probability