U9 TOPIC 2

Question 1

Sets - why bother?

Answer 1

Formalises the idea of grouping objects together and viewing them as a single entity,
This way a set becomes an abstraction
Laws governing sets form part of basis for Boolean algebra
Many program languages support sets as an abstract data type

Question 2

Terminology

Answer 2

Set is a well defined collection of objects
Objects are members or elements
A set is unordered
Each member in set can only occur
once
Set is denoted by capital letter (usually)
Member is denoted by lower case letter (usually)

Question 3

Examples of Sets

Answer 3

Set X contains even numbers between 1-99
Set C contains the colours in the rainbow
Blue is a member of C

Question 4

Listing each member

Answer 4

A set can be defined by listing every member
The members are enclosed by {}
The members are separated by a comma
Example - {red, orange, yellow}

Question 5

What does this common set represent?
{0, 1, 2, …}

Answer 5

N . Set of Natural numbers

Question 6

What does this common set represent?
{1, 2, 3, …}

Answer 6

Z^+ . Set of positive integers

Question 7

What does this common set represent
{…, -2, -1, 0, 1, 2, 3, …}

Answer 7

Z . Set of all integers

Question 8

What does this common set represent?
{2/11 , 4/25}

Answer 8

Q . Set of rational numbers (expressed as fractions)

Question 9

What does this common set represent?
{2.1 , 3.14, …}

Answer 9

R . Set of real numbers

Question 10

Is a member of Z also a member of Q?

Answer 10

Yes, because the number 12 for example, can be written as 12/1

Question 11

Describe an empty set?

Answer 11

One with no members

Question 12

How might the empty set be represented?

Answer 12

{ } or ∅

Question 13

How many different empty sets are there?

Answer 13

Just one

Question 14

How could you define the set of all girls born in 2000?

Answer 14

We need a new notation for this.

Question 15

what does expression x ∈ S mean?

Answer 15

“x is a member of the set S”

Question 16

What does expression x ∉ S mean?

Answer 16

“X is not a member of the set S”