Basic Set Theory Definitions and Operations

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Define what is a set and give an example.

A set is a well-defined collection of distinct objects. Example: Set of even numbers less than 10: {2, 4, 6, 8}

What is the difference between equal sets and equivalent sets?

Equal sets have exactly the same elements, while equivalent sets have the same number of elements.

Define what is a universal set and provide an example.

A universal set contains all possible elements that are under consideration in a particular context. Example: Universal set of all students in a school.

Explain the concept of complement of a set with an example.

The complement of a set includes all elements that are not in the set but are in the universal set. Example: Complement of set A is denoted as A' and includes all elements not in set A. Signup and view all the answers

What is the intersection of two sets and how is it represented?

The intersection of two sets is the set of elements that are common to both sets. It is represented by the symbol '∩'. Signup and view all the answers

Define what is a singleton set and provide an example.

A singleton set is a set with only one element. Example: Singleton set of the number 5: {5} Signup and view all the answers

Define an infinite set and provide an example.

An infinite set is a set with elements that cannot be counted up to its last element. An example is the set of natural numbers. Signup and view all the answers

Explain the concept of a finite set with an example.

A finite set is a set whose elements can be counted. An example is a set of students in a school. Signup and view all the answers

What is an empty (null) set? Provide an example to illustrate.

An empty (null) set is a set that has no elements. For example, the set of real numbers whose square is -1 is an empty set. Signup and view all the answers

Differentiate between finite and infinite sets. Provide a brief explanation.

Finite sets have a limited number of countable elements, while infinite sets have an endless number of uncountable elements. Signup and view all the answers

Why is the set of real numbers whose square is -1 considered an empty set?

The set of real numbers whose square is -1 is empty because there is no real number that satisfies this condition. Signup and view all the answers

Explain the significance of the symbol $ othing$ in representing a set.

The symbol $ othing$ represents an empty (null) set, indicating that the set contains no elements. Signup and view all the answers

Define a finite set. What distinguishes it from an infinite set?

A finite set can be counted, while an infinite set cannot be counted. Signup and view all the answers

Explain the concept of a complement of a set. How is it related to the universal set?

The complement of a set is the set of elements in the universal set but not in the set itself. It is denoted as Ac = U - A. Signup and view all the answers

What is the intersection of two sets? How is it defined?

The intersection of two sets is a set of elements that belong to both sets. Signup and view all the answers

Describe the concept of a subset in sets theory. How does it relate to set elements?

A set A is a subset of set B if every element of A is also an element of B. Signup and view all the answers

Explain the difference between a subset and a proper subset of a set.

A subset can be the same as the original set, while a proper subset must be a subset but not equal to the original set. Signup and view all the answers