Description of a set

We describe sets either by using words, by listing or by formula. For example if set A is a set of even numbers, we can describe it as follows:

1. By using words: A = {even numbers}
2. By listing: A = {2, 4, 6, 8, 10,...}
3. By formula: A = {x: x = 2n, where n = 1,2,3,…} and is read as A is a set of all x such that x is an even number.

Describe the following set by listing: N is a set of Natural numbers between 0 and 11

Solution

N = {1,2,3,4,5,6,7,8,9,10}

Write the following named set using the formula: O is a set of Odd numbers:

Solution

O = {x: x = 2n – 1, whereby n = 1,2,3….}

Write the following set in words: W = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

Solution

W = {whole numbers} or W is a set of whole numbers.

The objects in a set are called the members of the set or the elements of the set.

A set should satisfy the following:

1. The members of the set should be distinct. (not be repeated)
2. The members of the set should be well-defined. (well-explained)

In question 1 to 3 list the elements of the named sets.

1. A={x: x is an odd number < 10}
2. B={days of the week which begin with letter S}
3. C={prime numbers less than 13}

Solution

1. A={1,3,5,7,9}
2. B={Saturday, Sunday}
3. C={2,3,5,7,11}

To describe a small set, we list its members between curly brackets {, }:

• {2, 4, 6, 8}
• {England, France, Iran, Singapore, New Zealand}
• {David Beckham}
• {} (the empty set, also written ∅)

We write a ∈ X to express that a is a member of the set X. For example 4 ∈ {2, 4, 6, 8}. a ∉ X means a is not a member of X.