Question

find the complement of the set given that u = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. (enter your answers as a comma - separated list.) {x | x ∈ n and x < 6}

Explanation:

Step1: Define the given set

First, write out the set $\{x \mid x \in \mathbb{N} \text{ and } x < 6\}$. Since $\mathbb{N}$ (natural numbers) here includes 0 (as the universal set starts with 0), this set is $\{0, 1, 2, 3, 4, 5\}$.

Step2: Identify universal set

The universal set $U = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$.

Step3: Find the complement

The complement of a set contains all elements in $U$ not in the given set. Subtract the given set from $U$:
$U - \{0, 1, 2, 3, 4, 5\} = \{6, 7, 8, 9\}$

Answer:

6, 7, 8, 9