A set is defined as a collection of ___ objects.

Well-defined

If A = {F, O, L, W}, how many distinct elements are in the set A?

4

A collection of all even natural numbers can be represented as(in set builder form) ___ 

E = {2n | n ∈ N}

True or False: The collection of all natural numbers less than 100 is a well-defined set.

True

In roster form, the set of the first five natural numbers is represented as ___ in Roaster Form and in set builder form as {x | x is a natural number and x ≤ 5}.

{1, 2, 3, 4, 5}

The set of all whole numbers is an ___ set.

Infinite

What is a singleton set?

A set containing only one element is called a singleton set.

Example: 

A={7} is a singleton set

Two sets A and B are said to be equivalent if _____

They have the same number of elements
For Example:
The following A and B sets are equivalent because they have the same number of elements

If n(A) = n(B), then A and B are ___ but not necessarily ___.

Equivalent; equal

True or False: The empty set is a subset of every set.

True. The empty set is considered a subset of every set.

If a set A has 6 elements, how many total subsets does it have?

A set with n elements has 2ⁿ subsets. Therefore, if A has 6 elements, the total number of subsets is 2⁶, which equals 64.

If a set has n elements, the number of subsets is given by ___ and the number of proper subsets is given by ___.

2ⁿ for subsets and 2ⁿ - 1 for proper subsets

True or False: An improper subset contains at least one element from the original set.

False. An improper subset contains all elements of the original set.

True or False: If set C = {2, 4, 6} and set D = {2, 4, 6, 8}, then set D is a proper subset of set C.

False. Set D is not a proper subset of set C because it has an additional element (8) that is not in set C.

The universal set is defined as the set that contains all possible elements relevant to a given context. True or False?

True

If A = {1, 3, 5, 7} and B = {2, 4, 6, 8}, then the universal set N that contains all elements of A and B is ___ 

N = {1, 2, 3, 4, 5,6,7,8}

 If set A has 5 elements and set B has 3 elements, with 2 elements common to both sets, how many unique elements are there in the union of sets A and B?

The number of unique elements in the union of sets A and B is calculated as follows: |A ∪ B| = |A| + |B| - |A ∩ B|. Thus, |A ∪ B| = 5 + 3 - 2 = 6.

The union of sets A and B is represented as A ∪ B, and it includes all elements from both sets. True or False?

True

If A = {1, 2, 3, 4, 5, 6} and B = {2, 4, 6, 8}, then A ∩ B = ___ and A – B = ___.

A ∩ B = {2, 4, 6} and A – B = {1, 3, 5}

The intersection of two sets A and B consists of elements that are ___ in both sets.

Common

If A ∪ φ = A, this property is known as the ___ law.

Law of identity element

What is the relationship between A – B and B – A?

A – B ≠ B – A; they are not equal.