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Misc 19 - Number of binary operations on {a, b} are - Miscellaneous

Misc, 19 - Chapter 1 Class 12 Relation and Functions - Part 2
Misc, 19 - Chapter 1 Class 12 Relation and Functions - Part 3

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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

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.