Answer to Question #234311 in Math for Lenlen

Question

given that R denotes the set of all real numbers, Z the set of all integers, and Z' the set of all positive integers and Z the set of all negative integers, describe each of the following sets. a. {X€R| -5<x<1} b. {X€Z| -5<x<1} c. {X€Z'|-5<x<1} d. {X€Z| -5<x<1}

Answer 1

a. $\{X\in \R|-5<x<1\}$

All real numbers in the interval $X\in(-5, 1).$ There are infinite number of elements.

b. $\{X\in \Z|-5<x<1\}$

$X\in\{-4, -3, -2, -1, 0\}.$ There are 5 elements.

c. $\{X\in \Z^+|-5<x<1\}$

$X\in\{\empty\}.$ There are no elements.

d. $\{X\in \Z^-|-5<x<1\}$

$X\in\{-4, -3, -2, -1\}.$ There are 4 elements.