Which of the following statements is true about elements and sets?
The element of a set can never itself be a set.
The elements of every set are always themselves sets.
A set can be the element of another set.
The two terms are synonymous.
How many elements are in the set {a, {b, c}, d}?
4
2
3
1
Which of the following represents the set of all even positive integers less than 10?
{2, 4, 6, 8}
{0, 2, 4, 6, 8}
{2, 4, 6, 8, 10}
{0, 2, 4, 6, 8, 10}
Which of the following describes the light blue portion of the Venn diagram shown above?
B - A
A - B
A ∩ B - A ∪ B
A ∪ B - A ∩ B
Assume |A| = 3 and |B| = 4, what is |A × B|?
24
18
12
7
For which of the following pairs of sets is the relationship A ⊆ B ∧ A ⊂ B true?
A = {2, 5, 8, 10} and B = {2, 5, 8, 10}
A = {2, 5, 10} and B = {2, 3, 5, 8, 10}
A = {2, 3, 5, 8, 10} and B = {2, 3, 8, 10}
A = {2, 5, 8, 10} and B = {2, 3, 8, 10}
Assuming U represents the universal set and S represents any set, which of the following is a correct set property?
S ∪ ∅ = S
S ∩ ∅ = S
S ∩ U = U
S ∪ U = S
Assume that {A₁, A₂} is a partition of a set A. Which of the following is not always true?
A₁ ∩ A₂ = ∅
A₁ ∪ A₂ = A
A₁ ⊆ A
A₁ ⊂ A₂
Assuming an alphabet Σ = {a, b}, which of the following describes Σ⁰?
∅
{λ}
{a, b}
{a}
How many elements are in the power set of the empty set?
0
1
4
2