Set notation

Question 1

What is a set?

Answer 1

A collection of objects or numbers

Question 2

What are the objects in a Set called?

Answer 2

Members or elements of the set

Question 3

A = {1,2,3,4} means what?

Answer 3

Means set A with the elements 1,2,3,4

Question 4

3 € (only one line) A means what?

Answer 4

Means 3 is an element/member of set A

Question 5

curly E with a little dash on the tail means what?

Answer 5

Means the universal set. It is the set containing all elements, everything in the set.

Question 6

Ø means what?

Answer 6

Means the empty set. A set with no elements.

Question 7

Draw a vein diagram showing what AnB would look like

Answer 7

Only cross section is shaded

Question 8

AnB means what?

Answer 8

A intersection B, where the two cross over. Everything that’s A and B

Question 9

Draw a vent diagram showing AUB

Answer 9

Middle and both circles are shaded

Question 10

What does AUB mean?

Answer 10

A union b, everything that’s either A or B

Question 11

Draw a ven diagram showing A’

Answer 11

Middle and A circle aren’t shaded, B and universe is

Question 12

What does A’ mean?

Answer 12

A complement, everything that’s Not A

Question 13

a) List the elements of the following set: A - the factors of 24
b) true or false: i) 14 € A ii) 6 € A

Answer 13

A = {1,2,3,4,6,8,12,24}

I) false II) true

Question 14

True or false: if set C is the empty set, then 0 € C

Answer 14

False, C = {}

Question 15

Using set notation, list the elements of the set: P-The first four square numbers

Answer 15

P={1,4,9,16}

Question 16

Using set notation, list the elements of the set: M - the first 3 prime numbers

Answer 16

M={2,3,5}

Question 17

Using set notation, list the elements of the set: C-colours of the Union Jack flag

Answer 17

C={blue, white, red}

Question 18

True or false? If T = {factors of 12}then:

a) 4€T
b) 5€T
c) T€2

Answer 18

a) true
b) false
c) false: ‘T belongs to set 2’

Question 19

Draw a diagram and shade in AnB’

Answer 19

Only A shaded

A (and) intersection Not B

Question 20

Draw a vent diagram showing (A)

Answer 20

A and cross section

Question 21

Draw a venn diagram showing (A’)

Answer 21

B and outside universe

Question 22

Draw a venn diagram showing AuB

Answer 22

A and B

Question 23

Draw a venn diagram showing AuB’

Answer 23

Universe, a and cross section

‘A or not B’

Question 24

Draw a venn diagram showing (AuB)’

Answer 24

Everything outside of A and B

Question 25

Draw a venn diagram showing (B)

Answer 25

B and cross section

Question 26

Draw a venn diagram showing (AnB)

Answer 26

Cross section only

Question 27

Draw a venn diagram showing AnB'

Answer 27

A only

Question 28

Draw a venn diagram showing A'nB'

Answer 28

Everything outside of A and B

Question 29

Draw a venn diagram showing A'nB

Answer 29

B only

Question 30

In A is the numbers 1,3,9. In cross section is 2,6. In B is 8,4. In outer universe is 5,7. A = ?

Answer 30

{1,2,3,6,9}

Question 31

In A is the numbers 1,3,9. In cross section is 2,6. In B is 8,4. In outer universe is 5,7. B=?

Answer 31

{2,4,6,8}

Question 32

In A is the numbers 1,3,9. In cross section is 2,6. In B is 8,4. In outer universe is 5,7. AnB=?

Answer 32

{2,6}

Question 33

In A is the numbers 1,3,9. In cross section is 2,6. In B is 8,4. In outer universe is 5,7. AuB=?

Answer 33

{1,2,3,4,6,8,9}

Question 34

In A is the numbers 1,3,9. In cross section is 2,6. In B is 8,4. In outer universe is 5,7. A'=?

Answer 34

{8,5,4,7}

Question 35

In A is the numbers 1,3,9. In cross section is 2,6. In B is 8,4. In outer universe is 5,7. P(AnB)=?

Answer 35

2/9

Question 36

In A is the numbers 1,3,9. In cross section is 2,6. In B is 8,4. In outer universe is 5,7. P(AuB)=?

Answer 36

7/9

Question 37

In A is the numbers 1,3,9. In cross section is 2,6. In B is 8,4. In outer universe is 5,7. P(B')=?

Answer 37

5/9

Question 38

In A is the numbers 1,3,9. In cross section is 2,6. In B is 8,4. In outer universe is 5,7. P(A'nB)

Answer 38

2/9

Question 39

In A is the numbers 1,3,9. In cross section is 2,6. In B is 8,4. In outer universe is 5,7. P[(AuB)']=?

Answer 39

2/9

Question 40

``` Draw a Venn diagram for the information: Special E (universal)= {1,2,3,4,5,6,7,8,9,10} A={multiples of 2} AnB={2,6} AuB={1,2,3,4,6,8,9,10} ``` Also work out P(B)

Answer 40

P(B) = 5/10 = 1/2 In outer Universe: 5,7 A: 4,8,10 Cross section: 2,6 B: 1,3,9

Question 41

You have a Venn diagram. In Outer Universe is 0.1, A 0.2, cross section 0.3, B 0.4 Find the probability that A given B

Answer 41

0.3/0.7=3/7

Question 42

You have a Venn diagram. In Outer Universe is 0.1, A 0.2, cross section 0.3, B 0.4 Find P(B|A)

Answer 42

(Probability of B given A) | 0.3/0.5=3/5

Question 43

``` An insurance company records 200 accident claims. The table shows the speed of the car and weather conditions during the accident | wet| dry | total Speeding | 11 | 21 | 32 Not-speeding | 77 | 91 | 168 Total | 88 | 112 | 200 ``` Find the probability that the car is speeding given that it is wet

Answer 43

11/88 = 1/8

Question 44

``` An insurance company records 200 accident claims. The table shows the speed of the car and weather conditions during the accident | wet| dry | total Speeding | 11 | 21 | 32 Not-speeding | 77 | 91 | 168 Total | 88 | 112 | 200 ``` Find the probability that the car is not speeding given that it is dry?

Answer 44

91/112 = 13/16