Chapter 5 - Sets

Question 0

What are the items in a set called?

Answer 0

The items in a set are called ‘elements’. There symbol is a ‘squished capital e with one line and a curved side’.

Question 1

What is a set?

Answer 1

A set is a collection of clearly defined items.

Question 2

What are the rules of sets?

Answer 2

1. No elements will ever be listed twice.

2. The order of elements does NOT matter.

Question 3

What does ‘written as a rule mean’?

Answer 3

A={a,e,i,o,u}

Written as a rule: A={x|x is a vowel}

Question 4

What is a null set?

Answer 4

A null set is an empty set. Every set contains a null set.

Symbol: { } ~ nothing in it.

Question 5

What is a subset?

Answer 5

If A={1,2,3,4,5} and B={2,3,4} then B c A
Symbol: is a subset-squished ‘c’
is not a subset-squished ‘c’ with a slash through it
Examples:
{1,3,4} c {2,1,4,8,3} TRUE
{1,2,8} c/ {1,2,3,6,9} TRUE
{3,8,6,5,4} c/ {6,5,4} TRUE
{6,5,4} c/ {3,8,6,5,4} TRUE
{1,2,3} c {2,3,1} TRUE (Improper Subset!)
{ } c {8,3,2} TRUE (Improper Subset!)

Question 6

What is a proper subset?

Answer 6

All subsets which leave at least one element but also include one element.
e.g. A={1,2,3,4,5,6,7}
Write down one element subset of A
{2} or {4} or {5}

Question 7

What is an improper subset?

Answer 7

The set itself and the null set are called improper subsets. 
e.g. B={2,4,6,8,10}
Write down 2 improper subsets of B
1. { } 
2.  {2,4,6,8,10} or {10,8,6,2,4}

Question 8

What does ‘Intersection of Sets’ mean?

Answer 8

Symbol: Large 'n' with no tail
What is common between two sets
e.g. A={1,2,3,4,5,6}
B={3,5,8,9,10}
Q: AnB
A: AnB={3,5}

Question 9

What does ‘Union of Sets’ mean?

Answer 9

Symbol: U
Everything in two sets, but none are repeated.
e.g. A={1,2,3,4,5,6}
       B={3,5,8,9,10}
Q: AUB?
A: AUB={1,2,3,4,5,6,8,9,10}

Question 10

What does ‘cardinal number’ mean?

Answer 10

Symbol: #
The number of elements in a set.
e.g. A={1,2,3,4,5,6} #A=6
B={3,5,8,9,10} #B=5

Question 11

What does ‘set differences’ mean?

Answer 11

Symbol: \ 
e.g. A\B A kick out B 
e.g. A={1,2,3,4,5,6}
       B={2,4,6,7,8}
Find A\B
{1,2,3,4,5,6} \ {2,4,6,7,8} kick out anything from A thats in B
A\B={1,3,5}