Find which of the binary operations are commutative and which are associative.
Find which of the operations given above has identity.

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

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Video Transcript

Yeah. In this problem of relation and something we have to tell which operation have identity. So first days here. So first operation is given us message was doing A star be. So start with the binary operation on set Q. So start the binary operation on the given set cubes of racial number Q is a set of rational numbers. And first we have given a star B is equal to a minus B. And then second we have easter B is equal to a square plus B square. And then thought we have here. Lester B is equals to message A plus maybe a plus a way. And then fourth we have a pop star. B is B is equal to a minus B. Holy square. And then fifth part we have Esther B is equals to this is A B divided with four. And now and the part six we have we have a star way is equal to a B C square. And now we have to tell which one has identity, suppose we. So suppose here this operation has identity. So this would be a start identity. And this would be a minus identity. So this is not equals to A. So this is this doesn't have identity. Similarly here this will be a star I. And this would be a square plus I. Square. Which is not equals to a. Similarly here A star I. This will be A plus A. I. Which is not again equals to A. So this doesn't have an entity. And here that's what we age that I. So this would be a my next I. Holy square. This is not equals two. Again I but here when we put here a star I. So this would be equals two E. I. So here it could be A I. They were did with food. But here this is not equal to A. But here I could be possible. Or when this i is equal to say food. So say I E. Z equals two. Food. Then what would happen then? This would be a. Four. The four divided with four which equals to A. So here we have the identity. That is that age here, if B is equal to four. So here this is possible if B equals to four. And now for sixth part here again. So this would be A star I. So this is A. And ice cream. So this is not equal to it. So we have only one identity here, that is equals two. So here we can see that only when identity is there and which is only possible at we is equals to four. Or we can say identity is equal to four. So here we have identity equals to four and only one has the identity that age part five. Or we can say here B is equal to four. So identities for that means this is at we have we is equals to four.

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