Define set and list different types of sets with examples.

A set is a well-defined collection of distinct objects. These objects are called elements or members of the set. Sets are usually denoted by capital letters, and their elements are enclosed in curly braces $\{\}$.

• Empty Set (Null Set): A set containing no elements. It is denoted by $\emptyset$ or {}. Example: The set of all even prime numbers greater than 2. This set is $\emptyset$ because 2 is the only even prime number.

• Singleton Set: A set containing exactly one element. Example: The set of all even prime numbers. This set is $\{2\}$.

• Finite Set: A set with a countable number of elements. The process of counting the elements must come to an end. Example: The set of days in a week. This set is $\{\text{Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}\}$.

• Infinite Set: A set with an uncountable number of elements. The process of counting the elements would never end. Example: The set of all natural numbers. This set is $\{1, 2, 3, \dots\}$.

• Equal Sets: Two sets A and B are said to be equal if they contain exactly the same elements. Example: If $A = \{1, 2, 3\}$ and $B = \{3, 1, 2\}$, then $A = B$.

• Subset: A set A is a subset of set B if all elements of A are also elements of B. It is denoted by $A \subseteq B$. Example: If $A = \{1, 2\}$ and $B = \{1, 2, 3\}$, then $A \subseteq B$.

• Universal Set: The set of all elements under consideration in a particular context. It is usually denoted by $U$. Example: If we are discussing numbers, the set of all real numbers $\mathbb{R}$ could be a universal set.

• Disjoint Sets: Two sets are disjoint if they have no elements in common. Their intersection is an empty set. Example: If $A = \{1, 2, 3\}$ and $B = \{4, 5, 6\}$, then A and B are disjoint sets.