# Theory of Computation: Question Set – 01

#### What is a set?

A set is a collection of distinct objects, called elements or members, which can be anything from numbers and letters to other sets or more abstract entities.

#### What is the cardinality of a set?

The cardinality of a set is the number of distinct elements in the set. It can be a finite number, infinite, or even zero.

#### What is a subset?

A subset is a set whose elements are all contained in another set, called the superset. For example, {1, 2} is a subset of {1, 2, 3}.

#### What is the power set of a set?

The power set of a set is the set of all possible subsets of that set, including the empty set and the set itself. For example, the power set of {a, b} is {{ }, {a}, {b}, {a,b}}.

#### What is the union of two sets?

The union of two sets is the set of all elements that belong to at least one of the two sets. For example, the union of {1, 2} and {2, 3} is {1, 2, 3}.

#### What is the intersection of two sets?

The intersection of two sets is the set of all elements that belong to both of the two sets. For example, the intersection of {1, 2} and {2, 3} is {2}.

#### What is the complement of a set?

The complement of a set with respect to a universe set is the set of all elements in the universe set that do not belong to the original set. For example, the complement of {1, 2} with respect to {1, 2, 3} is {3}.

#### What is a Cartesian product?

The Cartesian product of two sets is the set of all possible ordered pairs of elements from the two sets. For example, the Cartesian product of {1, 2} and {a, b} is {(1,a), (1,b), (2,a), (2,b)}.

#### What is a partition of a set?

A partition of a set is a collection of non-empty subsets of the set, such that every element of the set belongs to exactly one of the subsets. For example, the sets {1, 2}, {3}, and {4, 5} form a partition of {1, 2, 3, 4, 5}.

#### What is the difference between a finite set and an infinite set?

A finite set is a set with a specific, limited number of elements, while an infinite set is a set with an uncountable number of elements. For example, the set of integers between 1 and 100 is a finite set, while the set of all integers is an infinite set.