Taking the set of natural numbers as the universal set,write down the complement of the following set:
$A = \{ x : x \in N \text{ and } 2x + 1 > 10 \}$
$A = \{ x : x \in N \text{ and } 2x + 1 > 10 \}$
The universal set is $U = N = \{1, 2, 3, 4, 5, \dots \}$.
Given set $A = \{ x : x \in N \text{ and } 2x + 1 > 10 \}$.
Solving the inequality: $2x > 9 \implies x > 4.5$.
Since $x \in N$,the set $A = \{5, 6, 7, 8, \dots \}$.
The complement of $A$ is $A' = U - A$.
$A' = \{ x : x \in N \text{ and } x \le 4.5 \}$.
Since $x \in N$,$A' = \{1, 2, 3, 4 \}$.
Given set $A = \{ x : x \in N \text{ and } 2x + 1 > 10 \}$.
Solving the inequality: $2x > 9 \implies x > 4.5$.
Since $x \in N$,the set $A = \{5, 6, 7, 8, \dots \}$.
The complement of $A$ is $A' = U - A$.
$A' = \{ x : x \in N \text{ and } x \le 4.5 \}$.
Since $x \in N$,$A' = \{1, 2, 3, 4 \}$.
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