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# Sets

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by

## R Sheehan

on 3 September 2014

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#### Transcript of Sets

Sets
Definition
A set is a
clearly defined
collection of objects.

For something to be clearly defined, it means that there is no doubt that an
element
belongs to a given set.
Examples:
The days of the week

The students in the class
Definition
An element is an item within a set.
The members of One Direction =
{ Niall Horan, Zayn Malik, Liam Payne, Harry Styles, Louis Tomlinson }
The best members of the Xmen are =
{ Cyclops, Beast, Storm }
Are these sets clearly defined?
Inside a set, we only list elements once.
"The letters of the word NAVAN could be listed in set form as
{N, A, V}, that is, no letter is repeated."

Textbook, page 73
Exercise 5.1

1. Say whether each of the following could be accurately described as a mathematical set:

(i) The counties of Leinster
(ii) The players on my football team
(iii) The tall pupils in my class
The elements within a set
1. symbol ϵ

2. Define by a rule

A = { Simon Cowell, Cheryl Cole, Louis Walsh, Mel B }

What is the rule here?
3. The null set is the set containing no elements.

The null set is denoted

-with set brackets without any elements inside
{ }
- or with the following symbol
Exercise 5.2
Q. 2
A = {x, y, z}, B = {3, 6, 9, 12}

Are the following true:

3 ϵ A

6 ϵ B
Let A = { M, A, T, H, E, I, C, S }
and let B = { T, A, M, I, C, S, E, H}

What can we say about these two sets?
Subsets
Definition: Set B is a subset of Set A if every element of B is also an element of A.

We use the symbol to denote a subset.
Full transcript