2 votes 2 votes why 4^10 is done. solution: Please explain the last portion why 4^ 10 is done. Set Theory & Algebra engineering-mathematics ace-test-series set-theory + – Overflow04 asked Aug 22, 2022 Overflow04 522 views answer comment Share Follow See all 2 Comments See all 2 2 Comments reply Kabir5454 commented Aug 22, 2022 reply Follow Share The binary relation is defined on a set $A$ which is a function from $A*A$ to $A$ . So , Number of element in $A*A$= $4*4=16$ So total number of binary operation is $4^{16}$. It consist of all the binary relations but we need only commutative . Commutative pair = no of symmetric relation which is first take all the reflexive pairs in $n$ ways then take symmetric pairs n(n-1)/2 . So total =n+n(n-1)/2= n(n+1)/2. putting n=4 ,we get 4*5/2=10 . so total we have $4^{10}$ commutative relation. 4 votes 4 votes yuyutsu commented Aug 23, 2022 reply Follow Share Okay I have a question here, what if they ask me for the no. of associative functions? 0 votes 0 votes Please log in or register to add a comment.
8 votes 8 votes Its a nice question [ Jiren ] answered Aug 22, 2022 [ Jiren ] comment Share Follow See all 0 reply Please log in or register to add a comment.