The ordered pairs in the relations on \( \{1,2,3\} \) corresponding to the matrix \( \left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 1\end{array}\right] \) is
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The matrix given is a \(3 \times 3\) matrix, which represents a relation on the set \(\{1, 2, 3\}\). Each element \(a_{ij}\) in the matrix indicates whether there is a relation from element \(i\) to element \(j\). Show more…
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Select the set that corresponds to the relation given in the matrix diagram below. Rows of the matrix are numbered 1 through 4 from top to bottom and columns are numbered 1 through 4 from left to right: {(2, 1), (2, 2), (3, 3), (4, 2)} {(1, 2), (2, 2), (2, 4), (3, 3)} {(1, 2), (2, 3), (2, 4), (3, 3)} {(2, 1), (2, 2), (3, 3), (3, 4)}
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List the ordered pairs in the relations on $\{1,2,3\}$ corresponding to these matrices (where the rows and columns correspond to the integers listed in increasing order). a) $\left[\begin{array}{lll}{1} & {0} & {1} \\ {0} & {1} & {0} \\ {1} & {0} & {1}\end{array}\right]$ b) $\left[\begin{array}{lll}{0} & {1} & {0} \\ {0} & {1} & {0} \\ {0} & {1} & {0}\end{array}\right]$ c) $\left[\begin{array}{lll}{1} & {1} & {1} \\ {1} & {0} & {1} \\ {1} & {1} & {1}\end{array}\right]$
Relations
Representing Relations
If R is the relation on A={1,2,3} such that (a,b)∈R, if and only if a+b is even. Find the relation matrix MR. Find also the relational matrices R−1, R¯, R2.
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