Q. 75.0( 1 Vote )

Prove that the operation * on the set

defined by A*B=AB is a binary operation.

Answer :

Given that * is an operation that is valid on the set and it is defined as given:A*B = A B.


According to the problem it is given that on applying the operation * for two given numbers in the set ‘M’ it gives a number in the set ‘M’ as a result of the operation.


A*BM ...... (1)


Let us take here aR, bR, cR and dR then,






Since aR and cR then acR


And also bR and dR then bdR.


ABR


The operation ‘*’ defines a binary operation on ‘M’.


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