by M Yass Aug 6 2016 updated Oct 4 2016

The union of two sets is the set of elements which are in one or the other, or both

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%%