Show that $$ is commutative and associative. Find the identity element for on $\mathrm{A}$, if any.
State whether the following statements are true or false. Justify.
(i) For an arbitrary binary operation $$ on a set $\mathbf{N}, a a=a \forall a \in \mathbf{N}$.
(ii) If $$ is a commutative binary operation on $\mathbf{N}$, then $a (b * c)=(c * b) * a$

Answer

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Algebra

NCERT Class 12 Part 1 - Math

Chapter 1

Relations and Functions

Section 4

Composition of Functions and Invertible Function

Discussion

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Video Transcript

in this problem of relation and function we have to state whether the following statement are true or false. So first statement is given us. So a statement number one is for any arbitrated operation. Start on natural number N. Well we have a Star A is equal to a. For every element of A which belongs to their given natural number N. So now here we didn't hear we have didn't specify the operation that a start, it is equal to a plus A. Or this is equals two A minus A. Or they say equals to a multiplied with him. So that's why. So that's why the given statement is not true, so this is false. Now, second statement is so second statement is if here a strategy community, binary operation on end. So here the star is communicating. They do binary operation. So this age binary operation. Community, binary operation on. And that means set of natural numbers. Then then we're here stuff be easter see is equal to see easter B. The start we have to show that this is true or false. So since decision binary operation, that means here, B and C equals two CNB. So since this advisory operation since the start is binary operation, that means here be star. See what we equals to see Star B. And now on end on the given set and and financial number then. Yes. Yeah, the C. Star we now we are taking here see the star B mr C. So this would be equal to the city equals to be starting and this is multiplied with. So from here we say that this is buying the operation so this can be replaced with here. So this will be a star beast. RC. From here we say that this LHs equals two oranges part. So we are taking taking the ICT and side part. So we have proved that L h S equals to RHS. So that's right. The statement is true, so our statement is true. So first statement it falls and the second statement is to.

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