Section 6.1 – Sets and Set Operations 1

Section 6.1

Sets and Set Operations

A collection of objects is called a set.

An object of a set is called an element.

Notation:

∈= “element of”

∉= “not an element of”

The set C = {x | 9

2=x} is in set builder notation.

The set C can also be written as follows: C = {-3, 3}.

Let A and B be two sets. If every element of A is also in B, A is said to be a subset of B.

Notation:

⊆ = “subset of”

⊆

/ = “not a subset of”

Example 1: Let C = {1,2,3,4,5,6}, D = {2,4,6}, E = {2,1,6,4,3,5}, and G = {1, 4, 6}.

Which of the following is/are true?

I. D⊆ C

II. E ⊆

/ C

III. D ⊆ G

The set A is a proper subset of a set B (Notation:

B

A⊂) if the following two

conditions hold.

1. BA ⊆

2. There exists at least one element in B that is not in A.

Example 2: Let G = {5,6,7,8,9,10}, H = {5,8,10}, I = {8, 5}, and J = {5,8}. Which of the

following is/are true?

I. H⊂G II. H⊂J III. J⊂H IV. I⊄J