Intersection

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

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,

  • \(\{1,2\} \cap \{2,3\} = \{2\}\)

  • \(\{1,2\} \cap \{8,9\} = \{\}\)

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