DSGT Module 1.2

What is a set in mathematics?

• A set is a mathematical operation.

• A set is a collection of similar objects.

• A set is a collection of distinct objects.

• A set is a single object.

How can sets be represented using roster notation?

• Sets are represented by using square brackets, e.g., [a, b, c].

• Sets can be shown as a list without any brackets, e.g., a, b, c.

• Sets are represented in roster notation by listing elements in curly braces, e.g., {a, b, c}.

• Sets are represented in roster notation by using parentheses, e.g., (a, b, c).

Define the union of two sets.

• The complement of a set A includes all elements not in A.

• The intersection of two sets A and B includes only the elements common to both.

• The union of two sets A and B is denoted as A ∪ B and includes all elements that are in A, in B, or in both.

• The difference of two sets A and B is the set of elements in A but not in B.

What is the intersection of two sets?

• The complement of a set is the set of elements not in the set.

• The difference of two sets is the set of elements in one set but not the other.

• The union of two sets is the set of all elements from both sets.

• The intersection of two sets is the set of elements common to both sets.

Explain the concept of a subset.

• A subset is a set that cannot be empty.

• A subset is a collection of unrelated items.

• A subset is a set that contains all elements of another set.

• A subset is a set that contains elements from another set.

What is the difference between a proper subset and a subset?

• A proper subset cannot be equal to the original set, while a subset can be equal.

• A proper subset must contain all elements of the original set.

• A subset can only contain elements that are not in the original set.

• A proper subset can include the original set as one of its elements.

Describe the complement of a set.

• The complement of a set A is the empty set.

• The complement of a set A includes all elements in A.

• The complement of a set A is the set of all elements in the universal set that are not in A.

• The complement of a set A is the set of all elements in the universal set that are also in A.

How do you denote the empty set?

• []

• ∅ or {}

• (empty)

• null

What is the Cartesian product of two sets?

• The Cartesian product is a single set containing all elements of A and B.

• The Cartesian product is the intersection of two sets.

• The Cartesian product of two sets A and B is A × B = {(a, b) | a ∈ A, b ∈ B}.

• The Cartesian product is the sum of two sets.

What is the symmetric difference of two sets?

• The symmetric difference is the set of elements that are in either of the sets but not in their intersection.

• The symmetric difference is the set of elements that are common to both sets.

• The symmetric difference is the union of two sets.

• The symmetric difference is the intersection of two sets.