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  • Let X be a non empty set n distinct elements. the total number of binary operations that can be defined on X is

Let X be a non empty set n distinct elements. the total number of binary operations that can be defined on X is

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Solution:

Given that n(X) = n , By definition , a binary opretion is a mapping

\ o:X imes X ightarrow X,Defined by \ (x,y) ightarrow xoy

Now, \ n(X imes X)=n^2

for each ordered pair \ (x,y)in X imes X, there are n choices .

Therefore , total number of binary operations=n^2

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Deependra Verma

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