Solution to Let R be a reflexive relation on a finite set A, and let MR be … - Sikademy
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Archangel Macsika

Let R be a reflexive relation on a finite set A, and let MR be the bit matrix representing R. Specify the value of the entries on the main diagonal.

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If R is a binary relation between the finite sets X and Y, that is R ⊆ X×Y, then R can be represented by the logical matrix M_R whose row and column indices index the elements of X and Y, respectively, 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\subset A\times A is reflexive relation, (x,x)\in R for all x\in A. Therefore, M_{i,i}=1 for all i\in\{1,...,|A|\}. Consequently, the value of all entries on the main diagonal is 1.

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Question ID: mtid-5-stid-8-sqid-3532-qpid-2231