Solution to Let R be a symmetric relation on a finite set A, and let MR be … - Sikademy
Author Image

Archangel Macsika

Let R be a symmetric relation on a finite set A, and let MR be the bit matrix representing R. Is MR necessarily a symmetric matrix? Why or why not?

The Answer to the Question
is below this banner.

Can't find a solution anywhere?


Get the Answers Now!

You will get a detailed answer to your question or assignment in the shortest time possible.

Here's the Solution to this Question

R is a binary relation on a finite set A , that is R ⊆ A×A, then R can be represented by the logical matrix M_R whose row and column indices index the elements of A such that the entries of M_R are defined by:

{\displaystyle m_{i,j}={\begin{cases}1&(x_{i},y_{j})\in R\\0&(x_{i},y_{j})\not \in R\end{cases}}}

Since R be a symmetric relation on a finite set A(x,y)\in R implies (y,x)\in R, and therefore m_{i,j}=1 if and only if m_{j,i}=1. It follows that M_R is necessarily a symmetric matrix.

Related Answers

Was this answer helpful?

Join our Community to stay in the know

Get updates for similar and other helpful Answers

Question ID: mtid-5-stid-8-sqid-3531-qpid-2230