This question was asked to me by a student of mine and I am not able to make any progress on this question.
Let $A=${1,2,3,4,5} , then which of the following is a binary operation?
(a) {((1,1),1),((1,2),1), ((1,3),1),((1,4),1) ,((1,5),1))}.
(b){((2,1),2),((2,2),2), ((2,3),2),((2,4),2) ,((2,5),2))}.
(c){((1,2),2),((1,3),3), ((1,4),4),((1,5),5) ,((1,1),1))}
(d) none of the above.
I tried using the definition of binary operation and function: Let $A$ be an non empty set then a function $f$ from $A \times A$ to $A$ is defined as a binary operation or a binary composition on $A$.
But I am not able to deciede using that I need help.