91Ó°ÊÓ

Find the transitive closure of each relation on \(A=\\{a, b, c\\}.\) $$f(a, b),(b, a)\\}$$

Find the transitive closure of each relation on \(A=\\{a, b, c\\}.\) $$\\{(b, a),(b, c),(c, b)\\}$$

Determine if each is a partial order. The relation | on \(\mathbf{Z}\)

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

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

The complement and inverse of a relation \(R\) from a set \(A\) to a set \(B,\) denoted by \(R^{\prime}\) and \(R^{-1}\) respectively, are defined as follows: \(R^{\prime}=\) \(\\{(a, b) | a R b\\}\) and \(R^{-1}=\\{(a, b) | b R a\\} .\) So \(R^{\prime}\) consists of all elements in \(A \times B\) that are not in \(R,\) whereas \(R^{-1}\) consists of all elements \((a, b)\) where \((b, a) \in R .\) Using the relations \(R=\\{(a, a),(a, b),(b, c),(c, c)\\}\) and \(S=\\{(a, a),(b, b),(b, c),(c, a)\\}\) on \(\\{a, b, c\\},\) find each. $$R^{-1}$$

The complement and inverse of a relation \(R\) from a set \(A\) to a set \(B,\) denoted by \(R^{\prime}\) and \(R^{-1}\) respectively, are defined as follows: \(R^{\prime}=\) \(\\{(a, b) | a R b\\}\) and \(R^{-1}=\\{(a, b) | b R a\\} .\) So \(R^{\prime}\) consists of all elements in \(A \times B\) that are not in \(R,\) whereas \(R^{-1}\) consists of all elements \((a, b)\) where \((b, a) \in R .\) Using the relations \(R=\\{(a, a),(a, b),(b, c),(c, c)\\}\) and \(S=\\{(a, a),(b, b),(b, c),(c, a)\\}\) on \(\\{a, b, c\\},\) find each. $$M_{R^{1}}$$

Find three triplets of positive integers that precede the triplet (2,3,5).

When is a relation on a set \(A\) not: Transitive?

Arrange the following words over the English alphabet in lexicographic order. mat, rat, bat, cat, eat, fat