We read your photo as:

List the following sets of whole numbers up to 20 in both listing and set-builder forms: composite, prime, even, odd, and square numbers.

Mathematics

ScanSolve AI Answer

Step-by-step solution

8 steps

Here are the sets formed from whole numbers up to 20 (i.e., {0,1,2,…,20}\{0, 1, 2, \dots, 20\}) in both listing and set-builder forms:

Part a(i)· 1 step

Set of composite numbers

  1. Identify composite numbers up to 20.

    Composite numbers are natural numbers greater than 1 that are not prime.
    Listing form:

    {4,6,8,9,10,12,14,15,16,18,20}\{4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20\}

    Set-builder form:

    {x∣x is a composite number and 0≤x≤20}\{x \mid x \text{ is a composite number and } 0 \le x \le 20\}

Part a(ii)· 1 step

Set of prime numbers

  1. Identify prime numbers up to 20.

    Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves.
    Listing form:

    {2,3,5,7,11,13,17,19}\{2, 3, 5, 7, 11, 13, 17, 19\}

    Set-builder form:

    {x∣x is a prime number and 0≤x≤20}\{x \mid x \text{ is a prime number and } 0 \le x \le 20\}

Part a(iii)· 1 step

Set of even numbers

  1. Identify even numbers up to 20.

    Even numbers are integers divisible by 2.
    Listing form:

    {0,2,4,6,8,10,12,14,16,18,20}\{0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20\}

    Set-builder form:

    {x∣x is an even number and 0≤x≤20}\{x \mid x \text{ is an even number and } 0 \le x \le 20\}

Part a(iv)· 1 step

Set of odd numbers

  1. Identify odd numbers up to 20.

    Odd numbers are integers not divisible by 2.
    Listing form:

    {1,3,5,7,9,11,13,15,17,19}\{1, 3, 5, 7, 9, 11, 13, 15, 17, 19\}

    Set-builder form:

    {x∣x is an odd number and 0≤x≤20}\{x \mid x \text{ is an odd number and } 0 \le x \le 20\}

Part a(v)· 1 step

Set of square numbers

  1. Identify square numbers up to 20.

    These are numbers that are the square of an integer.
    Listing form:

    {0,1,4,9,16}\{0, 1, 4, 9, 16\}

    Set-builder form:

    {x∣x=n2,n∈W,0≤n2≤20}\{x \mid x = n^2, n \in \mathbb{W}, 0 \le n^2 \le 20\}

Part a(vi)· 1 step

Set of cube numbers

  1. Identify cube numbers up to 20.

    These are numbers that are the cube of an integer.
    Listing form:

    {0,1,8}\{0, 1, 8\}

    Set-builder form:

    {x∣x=n3,n∈W,0≤n3≤20}\{x \mid x = n^3, n \in \mathbb{W}, 0 \le n^3 \le 20\}

Part a(vii)· 1 step

Set of multiples of 5

  1. Identify multiples of 5 up to 20.

    These are numbers that can be divided by 5 without a remainder.
    Listing form:

    {0,5,10,15,20}\{0, 5, 10, 15, 20\}

    Set-builder form:

    {x∣x is a multiple of 5 and 0≤x≤20}\{x \mid x \text{ is a multiple of } 5 \text{ and } 0 \le x \le 20\}

Part a(viii)· 1 step

Set of factors of 20

  1. Identify factors of 20.

    These are positive integers that divide 20 evenly.
    Listing form:

    {1,2,4,5,10,20}\{1, 2, 4, 5, 10, 20\}

    Set-builder form:

    {x∣x is a factor of 20}\{x \mid x \text{ is a factor of } 20\}
Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp