Ex 1.4, 2 (v) - Chapter 1 Class 12 Relation and Functions
Last updated at Dec. 16, 2024 by Teachoo
Binary Operations
Ex 1.4 ,1 (i)
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Chapter 1 Class 12 Relation and Functions
Serial order wise
- Ex 1.1
- Ex 1.2
- Examples
- Miscellaneous
- Case Based Questions (MCQ)
- Inverse of a function
-
Binary Operations
Transcript
Ex 1.4, 2 For each binary operation * defined below, determine whether * is commutative or associative. (v) On Z+, define a * b = π^π Check commutative * is commutative if a * b = b * a Since a * b β b * a * is not commutative a * b = π^π b * a = π^π Check associative * is associative if (a * b) * c = a * (b * c) Example Let a = 2, b = 3, c = 4 (a * b)* c = (π^π) * c = (π^π )^π a * (b * c) = a * (2^ππ) = 2^(π2^ππ ) (a * b)* c = (2 * 3) * 4 = (2^3) * 4 = 8 * 4 = 8^4 a * (b * c) = 2 * (3 * 4) = 2 * (3^4) = 2 * 81 = 2^81 Since (a * b) * c β a * (b * c) * is not an associative binary operation
