Set Notations

Question 1

What are the symbols for the empty/null set?

Answer 1

∅ or { }

Question 2

True or False: The union of two sets A and B is represented as A ∩ B.

Answer 2

False

Question 3

What does A ∪ B represent?

Answer 3

The union of sets A and B.

Question 4

Fill in the blank: The intersection of sets A and B is denoted as A _____ B.

Answer 4

∩

Question 5

What does A ⊆ B mean?

Answer 5

Set A is a PROPER subset of set B.

Question 6

Which notation represents the complement of set A?

Answer 6

A’

Question 7

True or False: A ∩ A’ = ∅.

Answer 7

True

Question 8

What is the symbol for the universal set?

Answer 8

U

Question 9

If A = {1, 2, 3} and B = {2, 3, 4}, what is A ∪ B?

Answer 9

{1, 2, 3, 4}

Question 10

What does A ∩ B mean?

Answer 10

The intersection of sets A and B.

Question 11

Fill in the blank: A set that contains all elements under consideration is called the _____ set.

Answer 11

universal

Question 12

What does A ⊄ B indicate?

Answer 12

Set A is not a subset of set B.

Question 13

If A = {x : x is an even number}, what does this notation represent?

Answer 13

Set A contains all even numbers.

Question 14

True or False: The notation A × B represents the Cartesian product of A and B.

explain why

Answer 14

true

Let:
• A = {1, 2}
• B = {x, y}

Then:
A x B = { (1, x), (1, y), (2, x), (2, y) }

Question 15

What is the Cartesian product of sets A = {1, 2} and B = {a, b}?

Answer 15

{(1, a), (1, b), (2, a), (2, b)}

Question 16

What does the notation |A| represent?

Answer 16

The number of elements in set A.

Question 17

Fill in the blank: The symbol for the power set of A is _____.

Answer 17

P(A)

Question 18

If A = {1, 2} and B = {2, 3}, what is A ∩ B?

Answer 18

{2}

Question 19

What does the notation A’ represent?

Answer 19

The complement of set A.

Question 20

What is the meaning of the notation A ∩ (B ∪ C)?

Answer 20

The intersection of set A with the union of sets B and C.

Question 21

Fill in the blank: The symbol for the difference of sets A and B is A _____ B.

Answer 21

\

Question 22

True or False: A ∪ ∅ = A.

Answer 22

True

Question 23

If A = {1, 2, 3} and B = {1, 2, 3, 4, 5},

A ⊆ B true or false?

Answer 23

True

Question 24

What does the notation {x : x > 0} represent?

Answer 24

The set of all x such that x is greater than 0.

Question 25

Fill in the blank: The symbol for the set difference of A and B is A _____ B.

Answer 25

\

Question 26

If U = {1, 2, 3, 4, 5} and A = {1, 2}, what is the complement A'?

Answer 26

{3, 4, 5}

Question 27

What does A ∪ B = B ∪ A demonstrate?

Answer 27

The commutative property of union.

Question 28

If A = {x : x is a prime number} and B = {2, 3, 5}, what is A ∩ B?

Answer 28

B, since all elements of B are prime.

Question 29

Element a belongs to set A. notation?

Answer 29

a ∈ A

Question 30

what does {x : x} mean?

Answer 30

“the set of all x such that x” — but there’s no condition given.

Question 31

Let A = {1, 2} what is the power set

Answer 31

P(A)= { ∅, {1}, {2}, {1,2} }

Question 32

how many subsets are in a power set?

Answer 32

P(A) = 2³=8

Question 33

power set 3 things to note

Answer 33

• Power set = all subsets • Always includes the empty set and the set itself • Total number of subsets = 2^n , where n = n(A)