Name: Number of Elements in a Set
Uploaded: 2019-07-19
Duration: 3 min 1 s
Description: What does the number of elements in the set refer to? Watch this interesting video to learn more about this new term in a set. Happy learning!

Question

Express the following set in set-builder notation (form):

{3, 6, 9, 12, 15}

Accepted Answer

We are given to express the following set in set-builder notation (form):
${3, 6, 9, 12, 15}$

Set builder notation is a mathematical notation of describing a set by listing its elements or demonstrating its properties that its members must satisfy.

In set-builder notation, we write sets in the form of
${x :$ properties of $x}$ or ${x |$ properties of $x}$

Here, the properties of $x$ are replaced by the condition that completely describes the elements of the set. The symbol $' :'$ or $' |'$ is used to separate the elements and properties. The symbols $' :'$ or $' |'$ is read as "such that" and the complete set is read as "the set of all elements $x$ " such that (properties of $x$ ). Here, we are using the variable $' x'$ to formulate the properties of the elements in the set.

In the given roster form of the set ${3, 6, 9, 12, 15}$ , we observe that all the elements of the set are natural numbers divisible by $3$ and the highest number $15$ is less than the number $18$ of the same kind.

Therefore, the given set written in set-builder notation is ${x : x$ is a natural number divisible by $3; x < 18}$ .

Express the following set in set-builder notation (form):
${3, 6, 9, 12, 15}$

Important Questions on Set Concepts

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