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. $$(A \wedge B) \vee(A \wedge C)$$

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

Using the equivalence relation \(\\{(a, a),(a, b),(b, a),(b, a),(c, c),(c, d)\\}\) on \(\\{a, b, c, d\\},\) find each equivalence class. \([c]\)

Using the equivalence relation \(\\{(a, a),(a, b),(b, a),(b, b),(c, c),(d, d)\\}\) on \(\\{a, b, c, d\\},\) find each equivalence class. $$[c]$$

Determine if the given elements are comparable in the poset \((A, |),\) where \(A=\\{1,2,3,6,9,18\\}\) and \(|\) denotes the divisibility relation. $$2,3$$

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. $$(A \vee B) \wedge(A \vee C)$$

Write an algorithm to find the adjacency list representation of a relation \(R\) on the set \(\\{1,2, \ldots, n\\}\) using: Its adjacency matrix \(A.\)

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. $$(A \vee B) \wedge(A \vee C)$$

Write an algorithm to find the adjacency matrix \(A\) of a relation on the set \(\\{1,2, \ldots, n\\}\) from its adjacency list representation.

Determine if the given elements are comparable in the poset \((A, |),\) where \(A=\\{1,2,3,6,9,18\\}\) and \(|\) denotes the divisibility relation. $$2,6$$