number of binary operations on set

Question

Answer 1

For number of binary operation (lets denote set with R) since 

|R|=4

binary operation( R X R ->R)  would be 4^(4*4) =4^16 

Answer 2

No of binary operation on a set with n element=n^(n^2)

here n=4

Ans 4^16

Answer 3

For number of binary operation with n variable are 2^{2^}n
Here Cardinality of R is 4.
No of Function = 2^{2^4} = 2¹⁶

 

Comments

you wrote the formula for the number of binary functions with n binary variables.

it's not correct.

please check.