Question

algebra i b-cr
1 2 3 4
the universal set is the set of rational numbers. s is the set of integers.
which represents $s^c$?
○ {x|x is a real number}
○ {x|x is a rational number}
○ {x|x is a rational positive number}
○ {x|x is a rational non-integer}

Explanation:

Step1: Define complement of a set

The complement \(S^c\) (or \(S'\)) of a set \(S\) within a universal set \(U\) is the set of all elements in \(U\) that are not in \(S\).

Step2: Identify given sets

Universal set \(U = \{\text{all rational numbers}\}\), \(S = \{\text{all integers}\}\).

Step3: Find elements of \(S^c\)

Elements in \(U\) but not in \(S\) are rational numbers that are not integers.

Answer:

{x|x is a rational non-integer}