Chapter 0.3: Sets

Question 1

What is a set?

Answer 1

An unordered collection of unique objects.

Question 2

What kind of values can a set have?

Answer 2

Any kind of value.

Question 3

Why is set Notation helpful?

Answer 3

Makes writing sets less verbose

Question 4

How does A = {1,2,3} read?

Answer 4

“A is the set containing the elements 1, 2, and 3.”

Question 5

How does a ∈ {a,b,c} read? ∉?

Answer 5

“a is an element of the set containing the letters a, b, and c.

Question 6

A = {1,b,{x, y, z}, ∅}, B = {1,b} and C = {x,y,z}. is B a subset of A? is C a subset of A?

Answer 6

Yes, No

Question 7

What are curly braces used for?

Answer 7

Enclosing the elements of a set

Question 8

What is ℕ?

Answer 8

Natural numbers set, not everyone includes 0, but the textbook does.

Question 9

What does “:” read? do?

Answer 9

“such that”

Separates the elements in the set from the conditions to be satisfied.

Question 10

How is this read: A = {x ∈ ℕ : ∃n ∈ ℕ(x = 2n) }? Can this be read more concisely?

Answer 10

“the set of all x in the natural numbers, such that there exists some n in the natural numbers for which x is twice n.”

“the set of all natural numbers that are even”

Question 11

What are substitute symbols for ∈ that mathematicians like to use?

Answer 11

“|” instead of “:”

Question 12

What is set builder notation?

Answer 12

Set building instructions that require a condition that elements must satisfy for inclusion

Question 13

In set builder notation, the ____ sometimes comes before the “:”.

Answer 13

Condition

Question 14

What is this symbol? ∅

Answer 14

the empty set is the set which contains no elements. Is a subset of every set

Question 15

What is this symbol? 𝓤

Answer 15

the universe set is the set of all elements

Question 16

What is this symbol? ℚ

Answer 16

the set of rational numbers

Question 17

What is this symbol? ℤ

Answer 17

the set of all integers {…, -3, -2, -1, 0, 1, 2, 3, …}

Question 18

What is this symbol? ℝ

Answer 18

the set of all real numbers. Any number that is rational or irrational

Question 19

What is this symbol? ℕ

Answer 19

the set of all natural numbers {0, 1, 2, 3, …}

Question 20

What is this symbol? P(A)

Answer 20

the power set of any set A that is the set of all subsets of A

Question 21

Read: {1,2,3}

Answer 21

The set containing the elements 1, 2, and 3.

Question 22

read: { x : x > 2 }

Answer 22

“x is the set of all x such that x is greater than 2”

Question 23

What is this symbol? ⊆

Answer 23

“Subet of”. A ⊆ B asserts that A is a subset of B: every element of A is also an element of B

Question 24

What is this symbol? ⊂

Answer 24

“Proper subset of”. A ⊂ B asserts that A is a proper subset of B: every element of A is also an element of B but A does not equal b

Question 25

What is this symbol? ∈

Answer 25

“is an element of” 2 ∈ {1,2,3} is an element of the set {1,2,3}

Question 26

What is this symbol? ∉

Answer 26

“is NOT an element of”. 4 ∉ {1,2,3} is not an element of the set {1,2,3}

Question 27

What is this symbol? ⋃

Answer 27

Union. A ⋃ B is the union of A and B: is the set containing all elements which are elements of A or B or both.

Question 28

What is this symbol? ⋂

Answer 28

Intersection. A ⋂ B is the intersection of A and B: the set containing all elements which are elements of both A and B

Question 29

What is this symbol? \

Answer 29

A \ B is the set difference between A and B: the set containing all elements of A which are not elements of B.

Question 30

What is this symbol? A'

Answer 30

(textbook has a line over A instead of an apostrophe after it) - the complement of A is the set of everything which is not an element of A.

Question 31

What is this symbol? |A|

Answer 31

the cardinality (or size) of A is the number of elements in A.

Question 32

explain ⊆ and ⊂ are analogous to ≤ and

Answer 32

⊆ means “is equal to or a subset of”

Question 33

What is P(A)?

Answer 33

The set of all possible subsets of A.

Question 34

What is Cardinality?

Answer 34

The number of elements in a set.

Question 35

What is another way of explain set difference?

Answer 35

A ⋂ B’ the intersection of A and the complement of B.

Question 36

Set operations produce \_\_\_\_\_\_.

Answer 36

Other sets.

Question 37

What is a cartesian product?

Answer 37

A set containing the pairings of every element in one set with each element in another set.

Question 38

\_\_\_\_ are great visual representations of operations on sets?

Answer 38

Venn Diagrams.

Question 39

Draw A ⋃ B?

Answer 39

Question 40

Draw A ⋃ B' or A \ B?

Answer 40

Question 41

Draw (B ⋂ C) ⋃ (C ⋂ A')

Answer 41