91Ó°ÊÓ

Draw the digraph of the relation. The relation \(R=\\{(1,2),(2,3),(3,4),(4,1)\\}\) on \\{1,2,3,4\\}

For the sequence t defined by \(t_{n}=2 n-1, \quad n \geq 1\). Find \(t_{3}\).

Determine whether the given relation is an equivalence relation on \(\\{1,2,3,4,5\\} .\) If the relation is an equivalence relation, list the equivalence classes. (In Exercises \(5-10\), \(x, y \in\\{1,2,3,4,5\\})\). \(\\{(x, y) \mid x\) and \(y\) are both even or \(x\) and \(y\) are both odd \(\\}\)

Determine whether the given relation is an equivalence relation on the set of all people. \(\\{(x, y) \mid x\) and \(y\) are the same height \(\\}\)

For the sequence t defined by \(t_{n}=2 n-1, \quad n \geq 1\). Find \(t_{7}\).

How can we quickly determine whether a relation \(R\) is antisymmetric by examining the matrix of \(R\) (relative to some ordering)?

Draw the digraph of the relation. The relation \(R=\\{(1,2),(2,1),(3,3),(1,1),(2,2)\\}\) on \(X=\\{1,2,3\\}\)

Determine whether each set in is a function from \(X=\\{1,2,3,4\\}\) to \(Y=\\{a, b, c, d\\} .\) If it is a function, find its domain and range, draw its arrow diagram, and determine if it is one-to-one, onto, or both. If it is both one- to-one and onto, give the description of the inverse function as a set of ordered pairs, draw its arrow diagram, and give the domain and range of the inverse function. $$ \\{(1, d),(2, d),(4, a)\\} $$

Determine whether the given relation is an equivalence relation on the set of all people. \(\\{(x, y) \mid x\) and \(y\) have, at some time, lived in the same country \(\\}\)

For the sequence t defined by \(t_{n}=2 n-1, \quad n \geq 1\). Find \(t_{100} .\)