The union of two sets \(A\) and \(B\), de­noted \(A \cup B\), is the set of things which are ei­ther in \(A\) or in \(B\) or both.

illustration of the output of the union operation

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

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

That is, Iff \(x\) is in the union \(C\), then ei­ther \(x\) is in \(A\) or \(B\) or pos­si­bly both.

todo: more lengthy ex­pla­na­tion for Math 2 level


  • \(\{1,2\} \cup \{2,3\} = \{1,2,3\}\)

  • \(\{1,2\} \cup \{8,9\} = \{1,2,8,9\}\)

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

  • \(\mathbb{R^-} \cup \mathbb{R^+} \cup \{0\} = \mathbb{R}\) (In other words, the union of the nega­tive re­als, the pos­i­tive re­als and zero make up all of the real num­bers.)