{x ∈ N | x ≤ 10 and x is divisible by 3}&nbsp;

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High School
Math Word Problem

Answered question

2022-03-20

{x ∈ N | x ≤ 10 and x is divisible by 3}

Answer & Explanation

user_27qwe

Skilled2023-04-24Added 375 answers

We are given the set of natural numbers x that are less than or equal to 10 and are divisible by 3. We can represent this set using set-builder notation as follows:

{x ∈ ℕ | x ≤ 10 and x mod 3 = 0}

Here, "ℕ" represents the set of natural numbers, "∈" means "belongs to," "mod" represents the modulo operation (i.e., the remainder when x is divided by 3), and "|" means "such that."

To find the elements of this set, we can simply list the natural numbers that satisfy the given conditions:

x = 3, 6, 9

Therefore, the set of natural numbers x that are less than or equal to 10 and are divisible by 3 is:

{x | x ∈ ℕ and x ≤ 10 and x mod 3 = 0} = {3, 6, 9}

Note that we can also use set-builder notation to represent this set as:

{x | x = 3k and k ∈ ℕ and x ≤ 10}

Here, "k" represents an arbitrary natural number. This notation expresses the fact that the elements of the set are all of the form 3k, where k is a natural number less than or equal to 3.

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