Definition:Set Intersection

Let $$S$$ and $$T$$ be any two sets.

The intersection of $$S$$ and $$T$$ is written $$S \cap T$$ and means the set which consists of all the elements which are contained in both of $$S$$ and $$T$$.

$$x \in S \cap T \iff x \in S \land x \in T$$

For example, let $$S = \left \{{1,2,3}\right\}$$ and $$T = \left \{{2,3,4}\right\}$$. Then $$S \cap T = \left \{{2,3}\right\}$$.

It can be seen that $$\cap$$ is an operator.

Some authors use the notation $$S T$$ or $$S \cdot T$$ for $$S \cap T$$, but this is non-standard and can be confusing.