91Ó°ÊÓ

Using the boolean matrices $$ A=\left[\begin{array}{ll} 1 & 1 \\ 0 & 0 \end{array}\right], B=\left[\begin{array}{ll} 0 & 1 \\ 1 & 0 \end{array}\right], \text { and } C=\left[\begin{array}{ll} 0 & 0 \\ 1 & 0 \end{array}\right] $$ find each. $$A \wedge(B \vee C)$$

Find the adjacency list representation of the relation with the given adjacency matrix.

Using the relations \(R=\\{(a, a),(a, b),(b, c)\\}\) and \(S=\\{(a, a),(b, b),(b, c),\) \((c, a) \\}\) on \(\\{a, b, c\\},\) find each. $$R^{3}$$

Find the adjacency matrix of the transitive closure of each relation \(R\) on \(\\{a, b, c\\}\) with the given adjacency matrix. $$\left[\begin{array}{lll} 0 & 1 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 0 \end{array}\right]$$

Using the boolean matrices $$A=\left[\begin{array}{lll}{1} & {0} & {1} \\ {0} & {0} & {0} \\ {1} & {1} & {0}\end{array}\right], B=\left[\begin{array}{lll}{0} & {0} & {1} \\ {0} & {1} & {0} \\ {1} & {0} & {0}\end{array}\right], \text { and } C=\left[\begin{array}{lll}{0} & {0} & {0} \\ {0} & {0} & {1} \\ {0} & {1} & {0}\end{array}\right]$$ find each. $$A \wedge(B \vee C)$$

In Exercises \(7-9,\) find the adjacency matrix of the transitive closure of each relation \(R\) on \(\\{a, b, c\\}\) with the given adjacency matrix. $$$\left[\begin{array}{lll}{0} & {1} & {0} \\ {0} & {1} & {1} \\ {1} & {0} & {0}\end{array}\right]$$

Find the connectivity relation of the relation on \(\\{a, b, c\\}\) with each adjacency matrix. $$\left[\begin{array}{lll} 1 & 0 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 0 \end{array}\right]$$

Find the connectivity relation of the relation on \(\\{a, b, c, d\\}\) with each adjacency matrix. $$\left[\begin{array}{llll} 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \end{array}\right]$$

Find the adjacency list representation of the relation with the given adjacency matrix.

Find the domain and range of each relation in Exercises \(1-6\).