Example 25 - Chapter 1 Class 12 Relation and Functions
Last updated at April 16, 2024 by Teachoo
To prove one-one & onto (injective, surjective, bijective)
One One function
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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
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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
Example 25 Consider the identity function IN : N → N defined as IN (x) = x ∀ x ∈ N. Show that although IN is onto but IN + IN : N → N defined as (IN + IN) (x) = IN (x) + IN (x) = x + x = 2x is not onto. IN : N → N IN (x) = x Let y = IN (x), such that y ∈ N So, y = x Since, x is natural number y is a natural number So, IN is onto. Now, IN + IN (x) = x + x = 2x ∴ IN + IN (x) = 2x Let y = IN + IN (x) , such that y ∈ N So y = 2x 2x = y x = 𝑦/2 If y = 1, x = 1/2 = 0.5 , which is not a natural number Hence, IN+ IN is not onto
