91Ó°ÊÓ

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

Determine if each is an equivalence relation. The relation \(\leq\) on \(\mathbb{R}\)

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. $$A \vee B$$

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

Determine if each is a partial order. The relation \(<\) on \(\mathbb{R}\)

List the elements in each relation from \(A=\\{1,3,5\\}\) to \(B=\\{2,4,8\\}\). $$\\{(a, b) | a < b\\}$$

Using the relations \(R=\\{(a, b),(a, c),(b, b),(b, c)\\}\) and \(S=\\{(a, a),(a, b),\) \((b, b),(c, a) \\}\) on \(\\{a, b, c |, \text { find } R \cup S \text { and } R \cap S\).

Using the relations \(R=\\{(a, b),(a, \mathrm{c}),(b, b),(b, c)\\}\) and \(S=\\{(a, a),(a, b)\) \((b, b),(c, a)\\}\) on \(\\{a, b, c\\},\) find \(R \cup S\) and \(R \cap S\).

List the elements in each relation from \(A=\\{1,3,5\\}\) to \(B=\\{2,4,8\\}\). $$\\{(a, b) | b=a+1\\}$$

Determine if each is an equivalence relation. The relation \(i s\) congruent to on the set of triangles in a plane.