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Ex 1.4, 12 - Chapter 1 Class 12 Relation and Functions
Last updated at Dec. 16, 2024 by Teachoo
Whether binary commutative/associative or not
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
- Binary Operations - Definition
-
Whether binary commutative/associative or not
- Binary operations: Identity element
- Binary operations: Inverse
Transcript
Ex 1.4, 12 State whether the following statements are true or false. Justify. (i) For an arbitrary binary operation * on a set N, a * a = a a * N. Let us define * a * b = a + b Calculating a * a Let a = b = 2 So, a * a = 2 * 2 = 2 + 2 = 4 2 So, a * a a Therefore, statement is false. Ex 1.4, 12 State whether the following statements are true or false. Justify. (ii) If * is a commutative binary operation on N, then a * (b * c) = (c * b) * a It is given that * is a commutative binary operation We need to check if a * (b * c) = (c * b) * a Solving R.H.S (c * b) * a = (b * c) * a = a * (b * c) = L.H.S. a * (b * c) = (c * b) * a Thus, statement is true.
