Set Notations

Question 1

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

Answer 1

∩

Question 2

Which notation represents the complement of set A?

Answer 2

A’

Question 3

True or False: A ∩ A’ = ∅.

Answer 3

True

Question 4

What is the symbol for the universal set?

Answer 4

U

Question 5

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

Answer 5

{1, 2, 3, 4}

Question 6

What does A ∩ B mean?

Answer 6

The intersection of sets A and B.

Question 7

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

Answer 7

universal

Question 8

What does A ⊄ B indicate?

Answer 8

Set A is not a subset of set B.

Question 9

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

Answer 9

Set A contains all even numbers.

Question 10

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

explain why

Answer 10

true

Let:
• A = {1, 2}
• B = {x, y}

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

Question 11

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

Answer 11

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

Question 12

What does the notation |A| represent?

Answer 12

The number of elements in set A.

Question 13

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

Answer 13

P(A)

Question 14

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

Answer 14

{2}

Question 15

What does the notation A’ represent?

Answer 15

The complement of set A.

Question 16

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

Answer 16

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

Question 17

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

Answer 17

\

Question 18

True or False: A ∪ ∅ = A.

Answer 18

True

Question 19

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

A ⊆ B true or false?

Answer 19

True

Question 20

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

Answer 20

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

Question 21

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

Answer 21

\

Question 22

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

Answer 22

{3, 4, 5}

Question 23

What does A ∪ B = B ∪ A demonstrate?

Answer 23

The commutative property of union.

Question 24

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

Answer 24

B, since all elements of B are prime.

Question 25

Element a belongs to set A. notation?

Answer 25

a ∈ A

Question 26

what does {x : x} mean?

Answer 26

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

Question 27

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

Answer 27

P(A)= { ∅, {1}, {2}, {1,2} }

Question 28

how many subsets are in a power set?

Answer 28

P(A) = 2³=8

Question 29

power set 3 things to note

Answer 29

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