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Q)

If A = {a, b}, then the number of binary operations that can be defined on

If A = {a, b}, then the number of binary operations that can be defined on A

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A)
A has 2 elements

⟹(A×A)has(a×b)=ab

A binary operation on A is a function from A×A into A.

Total no. of from (A×A) to A is

{n(A)}^n(A×A)=2^ab

Hence total no. of possible binary operation on 2^ab
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