# Set Symbols: How To Identify Them In Set Theory

Do you find it hard to recognise and interpret Set symbols in your mathematics exam?

In this lesson,

You will learn the ten basic Set symbols and how to interpret each of them with examples.

#### ALSO SEE: How To Solve Sets With Venn Diagram

Take note.

A link for you to practice exam questions on Sets is included at the bottom of this lesson.

## What is a set?

A set is a collection of similar or different items.

It can be represented with the capital letter of any alphabet.

The items in a set are called elements and each element is separated with a comma and all enclosed within a curly bracket.

EXAMPLE:

H = {c, u, r, l, y, b, r, a, c, k, e, t}.

## Set symbols and their meaning

See the basic set symbols and their meaning with examples.

### 1. Elements of a set

The elements, also called members, are those items present in a given Set.

It is represented with \in which means “IS AN ELEMENT OF” and \notin which means “IS NOT AN ELEMENT OF.”

EXAMPLE:

List the ELEMENTS of a Mathematical set.

M = {ruler, protractor, compass, set squares, eraser, divider, sharpener, pencils, pen, …}

### 2. Number of elements in a set

The number of elements in a Set is the total amount of items present in that Set.

It is represented with “n(set symbol) = amount of members.”

EXAMPLE:

The number of elements in a complete Mathematical set is written as n(M) = 13

### 3. Equal Sets

Two or more sets are equal if they contain the same elements.

This is represented with (=) which means “IS EQUAL TO” and (โ ) which means “IS NOT EQUAL TO.”

EXAMPLE:

If S = {b, a, d, c}, which of the following sets is equal to S?

• (a) P = {b, a, d, c, a, d}
• (b) Q = {d, a, c, e}
• (c) R = {first four letters of the alphabet}

P contains the same elements as in S, and even though letter a and d were repeated in P, they are to be counted only once. In other words, P = S

e \in Q but e \notin S, therefore Q โ  S

Lastly, R  = {first four letters of the alphabet} which are {a, b, c, d}. Therefore, R = S because the arrangement does not matter.

### 4. Empty set or null set

A set that contains no element is called an empty set or a null set.

It is represented with { } or โ.

EXAMPLE:

Set (T) = {pregnant men}

Of course,

Men don’t get pregnant so there will be no element in set T and that makes it an empty set. T = โ

### 5. Infinite set

An infinite set is a set that contains so many elements that it will be impossible to list all of its elements.

It is represented with three dots (โฆ) which means “AND SO ON.”

EXAMPLE:

Set (V) = {whole number that can be divided by 1}.

In other words,

V = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 โฆ}

### 6. Universal set

A universal set is the set that contains the elements of all the other sets in a given question.

It is represented with \mho

EXAMPLE:

\mho = {a, b, c, d, e, f, g}

### 7. Subset

Subsets are those other sets within the universal set.

It is represented with \subset which means “IS CONTAINED IN” and (ยข) which means “IS NOT CONTAINED IN.”

EXAMPLE:

\mho = {a, b, c, d, e, f, g}

• P = {b, a, d, c, a, d}
• V = {1, 2, 3, 4, 5, 6, 7, โฆ}

Set P is subset of \mho because P \subset \mho but V ยข \mho.

### 8. Union

The Union of Sets is the combination of the elements that two or more Sets have ALTOGETHER.

It is represented with \cup which means “UNION.”

EXAMPLE:

• P = {b, a, d, c, a, d}
• Q = {d, a, c, e}

P \cup Q = {a, b, c, d, e}

### 9. Intersection

The Intersection of Sets is the combination of the elements that two or more Sets have IN COMMON.

It is represented with \cap which means “INTERSECTION.”

EXAMPLE:

• P = {b, a, d, c, a, d}
• Q = {d, a, c, e}

P \cap Q = {a, c, d}

### 10. Complement of a set

The complement of a set are those elements present in the universal set but absent in the given subset.

It is represented with (‘) which means “COMPLEMENT.”

EXAMPLE:

• \mho = {a, b, c, d, e, f, g}
• Q = {d, a, c, e}.

Q’ = {b, f, g}

## Test yourself

Click on the link below to practice Mathematics past questions on Sets now.

GOOD LUCK.

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