Set Theory and Natural Numbers Quiz

Two sets are equal if they have the same elements. Order does not matter.

A set A is a subset of set B if every element in A is also in B. We use the symbol '⊂' to denote subset.

Every set is a subset of itself. Example: {1, 2} ⊂ {1, 2}.

The empty set (∅) is a subset of every set.

If sets A and B are subsets of each other (A ⊂ B and B ⊂ A), then they are equal sets.

The set of rational numbers (Q) is a subset of the set of real numbers (R).

Represents a set by listing all its elements, separated by commas and enclosed within curly braces. Example: {1, 2, 3}

Describes a set by stating a rule or property that its elements must satisfy. Example: {x : x is an even integer and 1 ≤ x ≤ 10}.

An element belongs to a set if it satisfies the condition specified in the set-builder form. We use the symbol '∈' to indicate membership. Example: 2 ∈ {x : x is a natural number}

An element does not belong to a set if it does not satisfy the condition specified in the set-builder form. We use the symbol '∉' to indicate non-membership. Example: 5 ∉ {x : x is an even number}

A way to describe a set by listing all its elements, separated by commas and enclosed within curly braces. Example: {1, 2, 3, 4, 5}

A method to define a set by stating a rule or property that its elements must satisfy. Example: {x : x is a natural number less than 6}

The set of all numbers that can be expressed as a fraction, where both the numerator and denominator are integers, and the denominator is not zero.

The set of all numbers that cannot be expressed as a fraction of integers. These numbers have infinite decimal representations that do not repeat.

A set of real numbers between two given numbers, known as endpoints. The endpoints themselves may or may not be included based on whether the interval is open or closed.

An interval that includes both endpoints.

An interval that excludes both endpoints.

A set of all elements considered in a particular context or study. It encompasses all relevant subsets within that context.

The difference between the endpoints of an interval.

A set of numbers that includes natural numbers, whole numbers, integers, rational numbers, and irrational numbers.

The universal set, denoted by U, encompasses all the elements that are relevant to a particular discussion or study. It acts like a container for all the possible elements.

The subset symbol (⊂) indicates that one set is contained within another. Everything in the smaller set is also found in the larger set.

If the subset symbol '⊄' is used between two sets, it means that the first set is not a subset of the second set. There must be at least one element in the first set that is not in the second set.

An element belongs to a set if it's included within the set's curly braces. We use the symbol '∈' to indicate this.

An interval is a continuous range of numbers on a number line. It is represented using parentheses or square brackets to indicate whether the endpoints are included or excluded.

In set-builder form, you define a set by listing the conditions its elements must satisfy. It looks like {x: x is [condition]} where x is a variable that represents any element in the set.

The empty set, denoted by ∅ or {}, is a set that contains no elements. It's a subset of every set.

A power set is a set of all the possible subsets of a given set. It includes the empty set and the original set itself.

The set of all real numbers that are not rational numbers. It includes all irrational numbers like pi and the square root of 2.

Two sets are disjoint if they have no elements in common.

The set containing all elements that are in the universal set but not in the given set.

The set of all prime numbers that are not divisors of 42. It includes all prime numbers except 2, 3, and 7.

The set containing all prime numbers that are divisors of 42. It includes {2, 3, 7}.

The set of all students in Class XI who are not girls. It includes all the boys in Class XI.

The complement of a set A is also a subset of the universal set U.

Finding the complement of a set involves identifying all elements in the universal set that are not present in the given set.

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

The intersection of two sets A and B, denoted as A ∩ B, is the set containing all elements that are common to both A and B.

The difference of two sets A and B, denoted as A - B, is the set containing all elements that are in A but not in B.

A set A is a subset of set B if every element in A is also present in B. We denote it as A ⊂ B.

The union of two sets A and B, where A is a subset of B (A ⊂ B), results in the set B. This happens because B already includes all the elements of A.

The intersection of two sets A and B, where A is a subset of B (A ⊂ B), results in the set A. This happens because A only contains elements that are also in B.