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Ex 1.1, 1 - Chapter 1 Class 12 Relation and Functions (Term 1)
Last updated at Aug. 11, 2021 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) You are here
Ex 1.1, 2
Ex 1.1, 3
Ex 1.1, 4
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, 1 Determine whether each of the following relations are reflexive, symmetric and transitive: (i) Relation R in the set A = {1, 2, 3 13, 14} defined as R = {(x, y): 3x y = 0} R = {(x, y): 3x y = 0} So, 3x y = 0 3x = y y = 3x where x, y A R = {(1, 3), (2, 6), (3, 9), (4, 12)} Check Reflexive If the relation is reflexive, then (a, a) R for every a A i.e. {1, 2, 3 13, 14} Since (1, 1) R ,(2, 2) R , (3, 3) R , . (14, 14) R R is not reflexive Check symmetric To check whether symmetric or not, If (a, b) R, then (b, a) R Here (1, 3) R , but (3, 1) R R is not symmetric Check transitive To check whether transitive or not, If (a,b) R & (b,c) R , then (a,c) R Here, (1, 3) R and (3, 9) R but (1, 9) R. R is not transitive Hence, R is neither reflexive, nor symmetric, nor transitive.
