What is a **set**? We usually refer to sets using a capital letter, e.g. A or B, and refer to their contents using curly brackets {,}.

Set theory is a kind of language, so let’s start by learning some of the key vocabulary that we will use.

**Exercise**

Let’s complete exercise 1 from pages 281 to 283 of the extended textbook:

The answers are below:

Now let’s start to think about solving problems in set theory using the formal notation.

**Example**

𝜖 = {1,2,3,…,12}, A={2,3,4,5,6}, B={2,4,6,8,10}

Find: (a) A∪B, (b) A∩B, (c) A’, (d) n(A∪B), (e) B’∩A.

**Exercise**

Let’s complete exercise 2 from pages 283 and 284 of the extended textbook:

The answers are below:

Now let’s try shading in some areas on Venn Diagrams

**Example**

**Exercise**

Let’s complete exercise 3 from pages 284 and 285 of the extended textbook:

The answers are below:

Now that we know the language of set theory, we can start to tackle some interesting questions that are best expressed (and resolved) using this language.

**Examples**

**Exercise**

Let’s complete exercise 4 from pages 287 to 289 of the extended textbook:

The answers are below: