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Question

Mathematics Question on Binary operations

If A=a,b,cA = \\{a,b,c\\}, then the number of binary operations on AA is

A

3

B

363^6

C

333^3

D

393^9

Answer

393^9

Explanation

Solution

A=a,b,cA=\\{a, b, c\\}
n(A)=3n(A)=3
Number of binary operations is
n(A)(n(A))2=3(32)=39n ( A )^{( n ( A ))^ 2}=3^{\left(3^ 2\right)}=3^{9}