Taking the set of natural numbers as the universal set,write down the complement of the following set:
$A = \{ x : x \text{ is a natural number divisible by } 3 \text{ and } 5 \}$
$A = \{ x : x \text{ is a natural number divisible by } 3 \text{ and } 5 \}$
(N/A) Let $U = N$ be the set of natural numbers.
The given set is $A = \{ x : x \text{ is a natural number divisible by } 3 \text{ and } 5 \}$.
Since a number divisible by both $3$ and $5$ is divisible by their least common multiple,which is $15$,we can write $A = \{ x : x \text{ is a natural number divisible by } 15 \}$.
The complement of set $A$,denoted by $A'$,is the set of all elements in $U$ that are not in $A$.
Therefore,$A' = \{ x : x \in N \text{ and } x \text{ is not divisible by } 15 \}$.
The given set is $A = \{ x : x \text{ is a natural number divisible by } 3 \text{ and } 5 \}$.
Since a number divisible by both $3$ and $5$ is divisible by their least common multiple,which is $15$,we can write $A = \{ x : x \text{ is a natural number divisible by } 15 \}$.
The complement of set $A$,denoted by $A'$,is the set of all elements in $U$ that are not in $A$.
Therefore,$A' = \{ x : x \in N \text{ and } x \text{ is not divisible by } 15 \}$.
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