The intersection of two sets \(A\) and \(B\), denoted \(A \cap B\), is the set of elements which are in both \(A\) and \(B\).

illustration of the output of an intersection

Formally stated, where \(C = A \cap B\)

$$x \in C \leftrightarrow (x \in A \land x \in B)$$

That is, Iff \(x\) is in the intersection \(C\), then \(x\) is in \(A\) and \(x\) is in \(B\).

For example,

  • \(\{1,2\} \cap \{2,3\} = \{2\}\)

  • \(\{1,2\} \cap \{8,9\} = \{\}\)

  • \(\{0,2,4,6\} \cap \{3,4,5,6\} = \{4,6\}\)