MATH: SET THEORY QUESTIONS AND
ANSWERS WITH SOLUTIONS 2024
Set - ANSWER A collection of objects. EXAMPLE: A deck of cards, A class, a collection of all even integers.
Element - ANSWER Each object in a set. EXAMPLE: the 2 of diamonds in a deck of cards is an element of
that set. **A= Set: deck of cards --> u=Element: 2 of diamonds -----> u E A** / ***A= Set: deck of cards --
> u=Element: Student -----> u E/ A***
Sets encountered in mathematics - ANSWER Z, 2Z, Q, R
Z= - ANSWER Integers: -4, -3, -2, -1, 0, 1, 2, 3, 4...etc
2Z= - ANSWER Even integers: 2, 4, 6, 8,...etc
Q= - ANSWER Rational numbers: number that can be written as a simple fraction. EX: 5 ---> 5/1
R= - ANSWER Real numbers: A set of numbers including counting, whole, integers, rational, and irrational
Examples elemental notations - ANSWER 4 E 2Z ; 16 E Z ; 3 E/ 2Z ; the root of 3 E/ Q
Defining a set - ANSWER Other than using words to define a set you can also define a set by LISTING OUT
THEIR ELEMENTS:
EXAMPLE:
N= Natural numbers
N = {0, 1, 2, 3, 4, ...}
Empty Set - ANSWER A set with no elements. Denoted by the the 0/ (0 with a slash through it) or by { }.
The empty set is ALWAYS a subset of every set
Equal Sets - ANSWER Two sets are equal if they contain exactly the same elements.
, EXAMPLE 1:
T= {a, b, c, d, e}
R = {e, d, a, c, b}
T=R
EXAMPLE 2:
T = {1, 2, 3, 4, 5}
R = {6, 7, 8, 9, 10}
T E/ R
Universal Set - ANSWER The set of all elements under consideration in a given discussion.
**U = Universal Set
Finite Set - ANSWER A set is finite if its cardinal number is a whole number.
EXAMPLE:
{a, b, c, d, e}
Infinite Set - ANSWER EXAMPLE:
{1, 2, 3, 4, 5, ...} Never ending.
Cardinal number - ANSWER Number of elements in a set.
EXAMPLE: A = {a, b, c, d, e}
n(A) = 5
Subset - ANSWER Given sets A and B, we say B is a SUBSET of A if every element of B is also an element
of A.
EXAMPLE:
A = {a, b, c, d}, and B = {a, e}
B is a subset ( _C_ : C with a dash underneath it) of A
ANSWERS WITH SOLUTIONS 2024
Set - ANSWER A collection of objects. EXAMPLE: A deck of cards, A class, a collection of all even integers.
Element - ANSWER Each object in a set. EXAMPLE: the 2 of diamonds in a deck of cards is an element of
that set. **A= Set: deck of cards --> u=Element: 2 of diamonds -----> u E A** / ***A= Set: deck of cards --
> u=Element: Student -----> u E/ A***
Sets encountered in mathematics - ANSWER Z, 2Z, Q, R
Z= - ANSWER Integers: -4, -3, -2, -1, 0, 1, 2, 3, 4...etc
2Z= - ANSWER Even integers: 2, 4, 6, 8,...etc
Q= - ANSWER Rational numbers: number that can be written as a simple fraction. EX: 5 ---> 5/1
R= - ANSWER Real numbers: A set of numbers including counting, whole, integers, rational, and irrational
Examples elemental notations - ANSWER 4 E 2Z ; 16 E Z ; 3 E/ 2Z ; the root of 3 E/ Q
Defining a set - ANSWER Other than using words to define a set you can also define a set by LISTING OUT
THEIR ELEMENTS:
EXAMPLE:
N= Natural numbers
N = {0, 1, 2, 3, 4, ...}
Empty Set - ANSWER A set with no elements. Denoted by the the 0/ (0 with a slash through it) or by { }.
The empty set is ALWAYS a subset of every set
Equal Sets - ANSWER Two sets are equal if they contain exactly the same elements.
, EXAMPLE 1:
T= {a, b, c, d, e}
R = {e, d, a, c, b}
T=R
EXAMPLE 2:
T = {1, 2, 3, 4, 5}
R = {6, 7, 8, 9, 10}
T E/ R
Universal Set - ANSWER The set of all elements under consideration in a given discussion.
**U = Universal Set
Finite Set - ANSWER A set is finite if its cardinal number is a whole number.
EXAMPLE:
{a, b, c, d, e}
Infinite Set - ANSWER EXAMPLE:
{1, 2, 3, 4, 5, ...} Never ending.
Cardinal number - ANSWER Number of elements in a set.
EXAMPLE: A = {a, b, c, d, e}
n(A) = 5
Subset - ANSWER Given sets A and B, we say B is a SUBSET of A if every element of B is also an element
of A.
EXAMPLE:
A = {a, b, c, d}, and B = {a, e}
B is a subset ( _C_ : C with a dash underneath it) of A
