subset

Examples of subset in the following topics:

• Total Number of Subsets

  • The total number of subsets is the number of sets with 0 elements, 1 element, 2 elements, etc.
  • The number of subsets containing $k$ elements is represented by ($n^k$).
  • The total number of subsets of a set with $n$ elements is $2^n$.
  • For example, how many subsets are in the set: $\left \{ P, Q, R, S, T, U \right \}$ ?
  • It has 6 elements, therefore, $2^n=2^6=64$ subsets.

• Sets of Numbers

  • A subset is a set whose every element is also contained in another set.
  • For example, if every member of set $A$ is also a member of set $B$, then $A$ is said to be a subset of $B$.

• Solving Systems of Linear Inequalities

  • If there is no intersection, then the two inequalities are either mutually exclusive, or one of the inequalities is a subset of the other.
  • For a simple example, $x>2$ and $x<1$ are mutually exclusive, whereas $x>2$ and $x>1$ has $x>2$ as a subset of $x>1$.

• Introduction to Complex Numbers

  • In this way, the set of ordinary real numbers can be thought of as a subset of the set of complex numbers.

• Theoretical Probability

  • For example, consider the number of distinct subsets of the integers $\left \{ 1, 2, \cdots , n \right \}$ that do not contain two consecutive integers.

• Functions and Their Notation

  • Functions can also be thought of as a subset of relations.