Ex 1.1, 7 - Chapter 1 Class 12 Relation and Functions
Last updated at April 16, 2024 by Teachoo
To prove relation reflexive, transitive, symmetric and equivalent
What is reflexive, symmetric, transitive relation?
You are here
You are here
Chapter 1 Class 12 Relation and Functions
Concept wise
- Relations - Definition
- Empty and Universal Relation
-
To prove relation reflexive, transitive, symmetric and equivalent
- Finding number of relations
- Function - Definition
- To prove one-one & onto (injective, surjective, bijective)
- Composite functions
- Composite functions and one-one onto
- Finding Inverse
- Inverse of function: Proof questions
- Binary Operations - Definition
- Whether binary commutative/associative or not
- Binary operations: Identity element
- Binary operations: Inverse
Transcript
Ex 1.1, 7 Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y): x and y have same number of pages} is an equivalence relation. R = {( x, y): x and y have same number of pages} Check reflexive If reflexive, then (x, x) ∈ R Book x and Book x have the same number of pages. Which is always true. ∴ Hence, R is reflexive Check symmetric If x and y have the same number of pages, then we can say that y and x have the same number of pages. Hence If (x, y) ∈ R, then (y, x) ∈ R ∴ R is symmetric. Check transitive If x and y have the same number of pages. & y and z have the same number of pages. then, x and z have the same number of pages. Hence , If (x, y) ∈ R & (y, z) ∈ R , then (x, z) ∈ R ∴ R is transitive Since R is reflexive, symmetric and transitive Hence, R is an equivalence relation.
