Introduction to Sets in Mathematics

Which of the following is the correct symbol for the union of two sets A and B?

If B is a subset of A, then A ∪ B = B.

What is the name of the property that states A ∪ B = B ∪ A?

The ______ of two sets A and B is represented by the symbol '∩' and includes only elements that are common to both sets.

Match the following terms to their corresponding definitions:

Which of the following sets is a subset of A = {1, 2, 3, 4, 5}?

What is the result of A ∪ φ, where φ represents the empty set?

The set {3, 6, 9, 12} can be written in set-builder form as {x : x is a ______ of 3, where x is a natural number}.

The intersection of two sets can be visualized using a Venn diagram.

The set {2, 4, 8, 16, 32} can be represented in set-builder form as {x : x = 2^n, where n is a natural number}.

What is the set-builder form of the set {5, 25, 125, 625}?

Which of the following sets is an infinite set?

Match the following sets with their descriptions:

The set {x : x - 5 = 0} can be written in roster form as {______}

The sets {x : x^2 = 25} and {x : x is an integral positive root of the equation x^2 - 2x - 15 = 0} are equal.

What are the elements of the set {n : n ∈ Z and n^2 ≤ 4}?

Who is credited with developing the theory of sets?

The concept of sets is only used in the field of mathematics.

What is the set of all natural numbers represented as?

The set of all ______ numbers is represented by the symbol Q.

Which of the following is NOT an example of a well-defined collection mentioned in the text?

Match the symbols with their corresponding sets:

What is the set of positive integers represented as?

The study of geometry, sequences, and probability does not require knowledge of sets.

Which of the following represents the set of all natural numbers less than 100 in set-builder form?

The set {1, 2, 3, 6, 9, 18} is equivalent to the set {x : x is a positive integer and is a divisor of 18}.

What is the roster form of the set {x : x is an integer and -3 ≤ x < 7}?

The set {0} can be described in set-builder form as {x : x is an integer and x + 1 = ______}.

Match the following sets described in roster form with their equivalent set-builder form.

Which of the following is NOT a set?

The symbol '∈' denotes that an element belongs to a set, and '∉' means it does not belong to a set.

What is the difference between a set and a collection?

What is the union of the sets X = {1, 3, 5} and Y = {1, 2, 3}?

The sets A - B, A ∩ B, and B - A are always disjoint.

Given A = {a, b} and B = {a, b, c}, what is A ∪ B?

If A ⊂ B, then A ∪ B = ______.

Match the following sets with their correct descriptions:

Which of the following pairs of sets are disjoint? (Select all that apply)

What is the difference between the sets A = {3, 6, 9, 12, 15, 18, 21} and B = {4, 8, 12, 16, 20} (A - B)?

If X = {a, b, c, d} and Y = {f, b, d, g}, then X ∩ Y = ______

Given a universal set U = {1, 2, 3, 4, 5, 6} and a set A = {2, 3}, what is the complement of A, denoted as A'?

For any sets A and B, the complement of the union of A and B is equal to the intersection of the complements of A and B. This is known as De Morgan's Law.

If U represents the universal set and A is a subset of U, what is the result of (A')'?

The ______ of two sets is the set containing elements that are in both sets.

Match the following set operations with their descriptions:

Given sets A = {1, 2, 3} and B = {2, 4, 5}, what is A ∪ B?

The complement of the empty set (φ) is equal to the universal set (U).

What is the name of the law that states (A ∪ B)' = A' ∩ B'?