1. Subsets

A set A is a subset of a set B if every element of A is also an element of B.

The notation is:

$$A\subseteq B$$

Example:

$$A=\{1,2\}$$

$$B=\{1,2,3,4\}$$

Since every element of A is contained in B,

$$A\subseteq B$$

Every set is a subset of itself:

$$A\subseteq A$$

The empty set is also a subset of every set:

$$\emptyset\subseteq A$$