Define and provide examples for the following types of sets: finite, infinite, null, unit, equivalent, equal, element of a set, and cardinality of a set.

Here are the meanings of the following terms with examples:

*a) Finite Set: A set that has a countable number of elements.
Example: The set of days in a week, $A = \{ \text{Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday} \}$.

*b) Infinite Set: A set that has an uncountable number of elements.
Example: The set of natural numbers, $N = \{ 1, 2, 3, \dots \}$.

*c) Null Set (or Empty Set): A set that contains no elements. It is denoted by $\emptyset$ or $\{ \}$.
Example: The set of all even prime numbers greater than 2, $B = \{ \}$.

*d) Unit Set (or Singleton Set): A set that contains exactly one element.
Example: The set of even prime numbers, $C = \{ 2 \}$.

*e) Equivalent Sets: Two sets are equivalent if they have the same number of elements (i.e., the same cardinality).
Example: If $A = \{ 1, 2, 3 \}$ and $B = \{ a, b, c \}$, then $A$ and $B$ are equivalent because both have 3 elements.

*f) Equal Sets: Two sets are equal if they contain exactly the same elements. The order of elements does not matter.
Example: If $A = \{ 1, 2, 3 \}$ and $B = \{ 3, 1, 2 \}$, then $A = B$.

*g) Element of a Set: An individual member or object belonging to a set.
Example: In the set $A = \{ 1, 2, 3 \}$, the number 1 is an element of set $A$, written as $1 \in A$.

*h) Cardinality of a Set: The number of distinct elements in a set. It is denoted by $n(A)$ for a set $A$.
Example: If $A = \{ a, b, c, d \}$, then the cardinality of $A$ is $n(A) = 4$.

*i) Complement of a Set: Given a universal set $U$ and a set $A$, the complement of $A$ (denoted $A'$ or $A^c$) is the set of all elements in $U$ that are not in $A$.
Example: If $U = \{ 1, 2, 3, 4, 5 \}$ and $A = \{ 1, 3 \}$, then $A' = \{ 2, 4, 5 \}$.

*j) Intersection of a Set: The intersection of two sets $A$ and $B$ (denoted $A \cap B$) is the set containing all elements that are common to both $A$ and $B$.
Example: If $A = \{ 1, 2, 3, 4 \}$ and $B = \{ 3, 4, 5, 6 \}$, then $A \cap B = \{ 3, 4 \}$.