Set Theory Quiz for Algebra Class 10

What is the set of irrational numbers represented by?

The sets {2, 3, 4, 5} and {3, 6} are disjoint sets.

The sets {a, e, i, o, u} and {a, b, c, d} are disjoint sets.

The sets {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.

The sets {2, 6, 10} and {3, 7, 11} are disjoint sets.

Given a universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and a subset A = {1, 3, 5, 7, 9}, what is the complement of A (A')?

If U is the universal set and A is a subset of U, then the complement of A is the set of all elements of U which are not the elements of A. This is denoted by ______

Match the following terms with their definitions:

The set of elements that belong to both set A and set B is called the ______ of A and B.

Match the set operations with their corresponding descriptions:

If two sets have no elements in common, they are called disjoint sets.

Which of the following is NOT a property of intersection?

Given sets A = { 1, 2, 3, 4 } and B = { 3, 4, 5, 6 }, find the difference A - B.

The difference of two sets is always commutative.

The set-builder notation for the difference of two sets A and B is A - B = {x: x ∈ A ______ x ∉ B}.

Which of the following Venn diagrams represents the difference of two sets A and B, where A is the larger circle and B is the smaller circle inside A?

Which of the following numbers is an example of a rational number?

The set of natural numbers is a subset of the set of irrational numbers.

What is the notation for the set of all real numbers that are not rational numbers?

The interval [2, 5] represents all real numbers between 2 and 5, ______ the endpoints.

Which of the following is a correct representation of the interval (–3, 5) in set-builder form?

Match the interval notation with its corresponding set-builder form:

The length of the interval (2, 7) is 5.

What is the universal set in the context of studying the system of numbers?

Georg Cantor is credited with the origination of modern set theory.

Who is considered to have first presented set theory as principles of logic?

What paradox, discovered by Bertrand Russell, led to a re-evaluation of the foundational assumptions of set theory?

The first axiomatization of set theory was published in 1908 by ______.

Match the mathematicians with their contributions to set theory:

Which of the following is NOT a De Morgan's Law?

The set of all sets is a valid concept in modern set theory.

What type of language is used to express most mathematical concepts and results in modern mathematics?

Which of the following sets is a subset of B = {2, 4, 6}?

If A ⊂ B and B ⊂ C, then A ⊂ C.

What is the union of sets A = {1, 2, 3} and B = {3, 4, 5}?

The set of all elements that are in set A but not in set B is called the ______ of A and B.

Which of the following is NOT a property of set operations?

Match the following set operations with their corresponding notations:

Which of the following statements accurately describes the union of two sets?

If set B is a subset of set A, then the union of A and B will always be equal to set A.

Given set A = {1, 2, 3, 4} and set B = {3, 4, 5}, what is the intersection of sets A and B, A ∩ B?

The symbol '∪' represents the ______ of two sets.

Match the following properties of the union operation with their corresponding laws.

Which of the following sets represents the intersection of sets X = {Ram, Geeta, Akbar} and Y = {Geeta, David, Ashok}?

The intersection of two sets always results in a set that is smaller than or equal to the size of the smaller of the two original sets.

Given set A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and set B = {2, 3, 5, 7}, what is the union of these sets, A ∪ B?