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Ex 1.1, 4 - Chapter 1 Class 12 Relation and Functions (Term 1)
Last updated at July 5, 2019 by Teachoo
To prove relation reflexive, transitive, symmetric and equivalent
What is reflexive, symmetric, transitive relation?
Example 4 Important
Ex 1.1, 6
Ex 1.1, 15 (MCQ) Important
Ex 1.1, 7
Ex 1.1, 1 (i)
Ex 1.1, 2
Ex 1.1, 3
Ex 1.1, 4 You are here
Ex 1.1, 5 Important
Ex 1.1, 10 (i)
Ex 1.1, 8
Ex 1.1, 9 (i)
Example 5
Example 6 Important
Example 2
Ex 1.1, 12 Important
Ex 1.1, 13
Ex 1.1, 11
Example 3
Ex 1.1, 14
Misc. 8 Important
Example 42 Important
Example 41
Chapter 1 Class 12 Relation and Functions
Concept wise
- Relations - Definition
- Empty and Universal Relation
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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, 4 Show that the relation R in R defined as R = {(a, b) : a b}, is reflexive and transitive but not symmetric. R = { (a,b) : a b } Here R is set of real numbers Hence, both a and b are real numbers Check reflexive We know that a = a a a (a, a) R R is reflexive. Check symmetric To check whether symmetric or not, If (a, b) R, then (b, a) R i.e., if a b, then b a Since b a is not true for all values of a & b Hence, the given relation is not symmetric Check transitive If a b, & b c , then a c If (a, b) R & (b, c) R , then (a, c) R Hence, the given relation is transitive Hence, R = {(a, b) : a b}, is reflexive and transitive but not symmetric
