Ex 1.1, 2 - Chapter 1 Class 12 Relation and Functions
Last updated at Dec. 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, 2 Show that the relation R in the set R of real numbers, defined as R = {(a, b) : a ≤ b2} is neither reflexive nor symmetric nor transitive R = {(a, b) : a ≤ b2} Checking for reflexive, If the relation is reflexive, then (a, a) ∈ R i.e. a ≤ a2 Let us check Hence, a ≤ a2 is not true for all values of a. So, the given relation it is not reflexive. Checking for symmetric, To check whether symmetric or not, If (a, b) ∈ R, then (b, a) ∈ R i.e., if a ≤ b2, then b ≤ a2 Since b ≤ a2 is not true for all values of a & b. Hence, the given relation is not symmetric Checking transitive To check whether transitive or not, If (a, b) ∈ R & (b, c) ∈ R , then (a, c) ∈ R i.e., if a ≤ b2, & b ≤ c2 then a ≤ c2 Since if a ≤ b2, & b ≤ c2 then a ≤ c2 is not true for all values of a, b, c. Hence, the given relation it is not transitive Therefore, the given relation is neither reflexive, symmetric or transitive
