Question

given that the universal set is all real numbers and set s is defined as the set of all x such that x is less than 5, which of the following is the complement of s?
s = {x | x < 5}
○ {x | x ≠ 5}
○ {6, 7, 8...}
○ {x | x > 5}
○ {x | x ≥ 5}

Explanation:

Step1: Recall complement definition

The complement of a set \( S \) (denoted \( S^c \)) within a universal set \( U \) is the set of all elements in \( U \) that are not in \( S \). Here, \( U \) is all real numbers, and \( S = \{x \mid x < 5\} \).

Step2: Determine elements not in \( S \)

We need all real numbers \( x \) where \( x \) is not less than 5. "Not less than 5" means \( x \geq 5 \) (since for real numbers, the negation of \( x < 5 \) is \( x \geq 5 \); this includes \( x = 5 \) and \( x > 5 \)).

Answer:

\(\{x \mid x \geq 5\}\) (the last option: \(\{x \mid x \geq 5\}\))