1.3 Subsets

What is a Subset?

Set $A$ is a subset of set $B$ if every element of $A$ is also in $B$.

Symbol: $A \subseteq B$

Read: "$A$ is a subset of $B$" or "$A$ is contained in $B$"

Think: If $B$ is a big box and $A$ is smaller, everything in $A$ must be in $B$.

The Subset Formula

If a set has $n$ elements, it has exactly $2^n$ subsets (including the empty set and the set itself).

Formula: Number of subsets = $2^n$

This is a powerful counting formula!