Show that the number of binary operations on {1,2} having 1 as the identity and having 2 as the inverse of 2 is exactly one.

Asked by snigdhaa | 16th Mar, 2013, 05:16: PM

Expert Answer:

Binary operation is a function from A x A to A.
So, binary operation on {1,2} will be a function from {1,2}x{1,2} to {1,2}.
Expand the set A x A. So, it is a function from {(1,1), (1,2), (2,1), (2,2)} to {1,2}.
Now, it is given that 1 is the identity for the desired binary operation.
Therefore,

Answered by  | 17th Mar, 2013, 10:45: PM

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