Chapter 0.3: Sets Flashcards

1
Q

What is a set?

A

An unordered collection of unique objects.

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2
Q

What kind of values can a set have?

A

Any kind of value.

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3
Q

Why is set Notation helpful?

A

Makes writing sets less verbose

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4
Q

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

A

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

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5
Q

How does a ∈ {a,b,c} read? ∉?

A

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

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6
Q

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?

A

Yes, No

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7
Q

What are curly braces used for?

A

Enclosing the elements of a set

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8
Q

What is ℕ?

A

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

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9
Q

What does “:” read? do?

A

“such that”

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

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10
Q

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

A

“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”

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11
Q

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

A

“|” instead of “:”

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12
Q

What is set builder notation?

A

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

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13
Q

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

A

Condition

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14
Q

What is this symbol? ∅

A

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

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15
Q

What is this symbol? 𝓤

A

the universe set is the set of all elements

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16
Q

What is this symbol? ℚ

A

the set of rational numbers

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17
Q

What is this symbol? ℤ

A

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

18
Q

What is this symbol? ℝ

A

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

19
Q

What is this symbol? ℕ

A

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

20
Q

What is this symbol? P(A)

A

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

21
Q

Read: {1,2,3}

A

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

22
Q

read: { x : x > 2 }

A

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

23
Q

What is this symbol? ⊆

A

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

24
Q

What is this symbol? ⊂

A

“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

25
Q

What is this symbol? ∈

A

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

26
Q

What is this symbol? ∉

A

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

27
Q

What is this symbol? ⋃

A

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.

28
Q

What is this symbol? ⋂

A

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

29
Q

What is this symbol? \

A

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

30
Q

What is this symbol? A’

A

(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.

31
Q

What is this symbol? |A|

A

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

32
Q

explain ⊆ and ⊂ are analogous to ≤ and

A

⊆ means “is equal to or a subset of”

33
Q

What is P(A)?

A

The set of all possible subsets of A.

34
Q

What is Cardinality?

A

The number of elements in a set.

35
Q

What is another way of explain set difference?

A

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

36
Q

Set operations produce ______.

A

Other sets.

37
Q

What is a cartesian product?

A

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

38
Q

____ are great visual representations of operations on sets?

A

Venn Diagrams.

39
Q

Draw A ⋃ B?

A
40
Q

Draw A ⋃ B’ or A \ B?

A
41
Q

Draw (B ⋂ C) ⋃ (C ⋂ A’)

A