set_theory_flashcards

Question 1

Set {}

Answer 1

An unordered collection of distinct objects, e.g., {apple, orange, banana}.

Question 2

Element of a Set ∈

Answer 2

An item in a set, denoted as ‘a ∈ A’ meaning ‘a is in A’.

Question 3

Empty Set Ø or {}

Answer 3

A set with no elements, denoted as Ø or {}.

Question 4

Finite Set

Answer 4

A set with a limited number of elements, e.g., {1, 2, 3}.

Question 5

Infinite Set

Answer 5

A set with an unlimited number of elements, e.g., {1, 2, 3, …}.

Question 6

Subset ⊆

Answer 6

A set where all elements are also in another set, denoted as A ⊆ B, e.g., {1, 2} ⊆ {1, 2, 3}.

Question 7

Proper Subset ⊂

Answer 7

A subset that is not equal to the set it is contained within, e.g., {1, 2} ⊂ {1, 2, 3}.

Question 8

Superset ⊇

Answer 8

A set containing all elements of another set, e.g., {1, 2, 3, 4} ⊇ {1, 2}.

Question 9

Universal Set

Answer 9

The set that contains all possible elements in a given context.
U={1,2,3,4}

Question 10

Complement
U={1,2,3,4}, A={1,2}
What is A’?

Answer 10

All elements not in a specified set, relative to the universal set, e.g., if U={1,2,3,4}, A={1,2}, then A’={3,4}.

Question 11

Union
{1,2,3} ∪ {2,3,4,5}

Answer 11

All elements from two sets, without ones that appear in both denoted A ∪ B, e.g., {1,2} ∪ {2,3} = {1,2,3,4,5}.

Question 12

Intersection
{1,2,3} ∩ {2,3,4}

Answer 12

Elements common to both sets, denoted A ∩ B, e.g., {1,2,3} ∩ {2,3,4} = {2,3}.

Question 13

Difference
{1,2,3} - {2,3}

Answer 13

Elements in one set but not the other, denoted A - B, e.g., {1,2,3} - {2,3} = {1}.

Question 14

Symmetric Difference
{1,2} ⊕ {2,3}

Answer 14

Elements in either set but not both, denoted A ⊕ B, e.g., {1,2} ⊕ {2,3} = {1,3}.

Question 15

Commutative Law (Union)
A ∪ B =?

Answer 15

A ∪ B = B ∪ A.

Question 16

Commutative Law (Intersection)
A ∩ B = ?

Answer 16

A ∩ B = B ∩ A.

Question 17

Associative Law (Union)
(A ∪ B) ∪ C = ?

Answer 17

(A ∪ B) ∪ C = A ∪ (B ∪ C).

Question 18

Associative Law (Intersection)
(A ∩ B) ∩ C =?

Answer 18

(A ∩ B) ∩ C = A ∩ (B ∩ C).

Question 19

Distributive Law (Intersection over Union)
A ∩ (B ∪ C) =?

Answer 19

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C).

Question 20

Distributive Law (Union over Intersection)
A ∪ (B ∩ C) =?

Answer 20

A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C).

Question 21

Identity Law (Union)
A ∪ Ø = ?

Answer 21

A ∪ Ø = A.

Question 22

Identity Law (Intersection)
A ∩ U =?

Answer 22

A ∩ U = A.

Question 23

Complement Law (Union)
A ∪ A’ = ?

Answer 23

A ∪ A’ = U.

Question 24

Complement Law (Intersection)
A ∩ A’ = ?

Answer 24

A ∩ A’ = Ø.

Question 25

Idempotent Law (Union)
A ∪ A =?

Answer 25

A ∪ A = A.

Question 26

Idempotent Law (Intersection)
A ∩ A =?

Answer 26

A ∩ A = A.

Question 27

Double Complement Law
(A’)’ =?

Answer 27

(A’)’ = A.

Question 28

De Morgan’s Law (Complement of Union)
(A ∪ B)’ = ?

Answer 28

(A ∪ B)’ = A’ ∩ B’.

Question 29

De Morgan’s Law (Complement of Intersection)
(A ∩ B)’ =?

Answer 29

(A ∩ B)’ = A’ ∪ B’.

Question 30

Cartesian Product
if A={1,2} and B={x,y}, then what is A × B?

Answer 30

The set of all ordered pairs from two sets, e.g., if A={1,2} and B={x,y}, then A × B = {(1,x), (1,y), (2,x), (2,y)}.

Question 31

Power Set
if A = {1, 2}, then 𝒫(A) is?

Answer 31

The set of all subsets of a set, including the empty set, e.g., if A = {1, 2}, then 𝒫(A) = {Ø, {1}, {2}, {1, 2}}.