91Ó°ÊÓ

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

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

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

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. \([a]\)

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

Write an algorithm to find the adjacency list representation of a relation \(R\) on the set \(\\{1,2, \ldots, n\\}\) using: The relation, given in terms of ordered pairs.

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

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. $$[b]$$

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

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. \([b]\)