Examples of subset in the following topics:
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- 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.
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- 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 $B$.
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- 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 $x>1$.
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- In this way, the set of ordinary real numbers can be thought of as a subset of the set of complex numbers.
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- For example, consider the number of distinct subsets of the integers $\left \{ 1, 2, \cdots , n \right \}$ that do not contain two consecutive integers.
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- Functions can also be thought of as a subset of relations.