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Question 12 (MCQ) - Binary Operations - Definition - Chapter 1 Class 12 Relation and Functions
Last updated at Dec. 16, 2024 by Teachoo
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
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Binary Operations - Definition
- Whether binary commutative/associative or not
- Binary operations: Identity element
- Binary operations: Inverse
Transcript
Misc 19 Number of binary operations on the set {a, b} are 10 (B) 16 (C) 20 (D) 8 A binary operation * on {a, b} is * : {a, b} × {a, b} → {a, b} {a, b} × {a, b} = {(a, a), (a, b), (b, a), (b, b)} So, * : {(a, a), (a, b), (b, a), (b, b)} → {a, b} We can define * as a * a = a , a * b = a , b * a = a & b * b = a We denote it as Similarly, there can be other combinations. we see all of them Combinations Total combinations = 16 By formula, Total combinations = 22 × Number of element of set = 22 × 2 = 24 = 16 Hence, B is the correct answer
