Let R1 and R2 be a relations on a set A represented by the matrices below: MR1=[010111100] MR2=[010011111] Find the matrix that represents R1∩R2

"Let R1 and R2 be a relations on..." solved and explained

Lloyd Allen

Answered question

2021-11-19

Let

R_{1}

and

R_{2}

be a relations on a set A represented by the matrices below:

M_{R 1} = [\begin{matrix} 0 & 1 & 0 \\ 1 & 1 & 1 \\ 1 & 0 & 0 \end{matrix}]

M_{R 2} = [\begin{matrix} 0 & 1 & 0 \\ 0 & 1 & 1 \\ 1 & 1 & 1 \end{matrix}]

Find the matrix that represents

R_{1} \cap R_{2}

Answer & Explanation

romancemrf

Beginner2021-11-20Added 14 answers

Consider the given matrices, $M_{R 1} = [\begin{matrix} 0 & 1 & 0 \\ 1 & 1 & 1 \\ 1 & 0 & 0 \end{matrix}] a n d M_{R 2} = [\begin{matrix} 0 & 1 & 0 \\ 0 & 1 & 1 \\ 1 & 1 & 1 \end{matrix}]$
Note that, the intersection $a \cap B$ is all elements that are both in A and in B.
The matrices representing each of the relations come together to form the matrix corresponding to the intersection of two relations.
$M_{R_{1} \cap R_{2}} = M_{R_{1}} \cap M_{R_{2}}$
$= [\begin{matrix} 0 \land 0 & 1 \land 1 & 0 \land 0 \\ 1 \land 0 & 1 \land 1 & 1 \land 1 \\ 1 \land 1 & 0 \land 1 & 0 \land 1 \end{matrix}]$
$= [\begin{matrix} 0 & 1 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 0 \end{matrix}]$
Hence, the matrix that represents $R_{1} \cap R_{2} i s = [\begin{matrix} 0 & 1 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 0 \end{matrix}]$

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