如何解决R的问题

Question

这个东西的意思是什么？

R o R o R o R = R o R o R

As I understand it means R of R of R of R is same as R of R of R But It seems there something more in discrete mathematics

Answer 1

让我们考虑在集合 S={1,2,3} 上定义的关系 R={(1,2),(2,3),(3,1)}。

R o R 计算如下

     R o R(1) = R(2) = 3
     R o R(2) = R(3) = 1
     R o R(3) = R(1) = 2

R o R = {(1,3),(2,1),(3,2)}

同样 R o R o R = {(1,1),(2,2),(3,3)}

R o R o R o R = {(1,2),(2,3),(3,1)}

for this example R o R o R o R = R

In case your question R o R o R o R = R o R o R, The relation R={(1,1),(2,2),(3,3)} satisfies the equation.

Answer 2

你是对的; 的意思：

R o R o R o R = R o R o R

这是：

R of R of R of R is equal to R of R of R

我们可以通过与 R 的逆组合，基于这个等式推断出更多关于 R 的性质：

R o R o R o R = R o R o R
(R^-1 o R^-1 o R^-1) o (R o R o R o R) = (R^-1 o R^-1 o R^-1) o (R o R o R)
(R^-1 o R^-1) o (R^-1 o R) o (R o R o R) = (R^-1 o R^-1) o (R^-1 o R) o (R o R)
(R^-1 o R^-1) o I o (R o R o R) = (R^-1 o R^-1) o I o (R o R)
(R^-1 o R^-1) o (R o R o R) = (R^-1 o R^-1) o (R o R)

您可以重复此过程并发现：

R = I

是唯一可接受的解决方案。