July 19, 2012, midnight by Rosalind Team

**Topics**:
Set Theory

## Forming New Sets

Just as numbers can be added, subtracted, and multiplied, we can manipulate sets in certain basic ways. The natural operations on sets are to combine their elements, to find those elements common to both sets, and to determine which elements belong to one set but not another.

Just as graph theory is the mathematical study of graphs and their properties, set theory is the mathematical study of sets and their properties.

If *either* *both*

Furthermore, if

Given: A positive integer

Return: Six sets:

10 {1, 2, 3, 4, 5} {2, 8, 5, 10}

{1, 2, 3, 4, 5, 8, 10} {2, 5} {1, 3, 4} {8, 10} {8, 9, 10, 6, 7} {1, 3, 4, 6, 7, 9}

## Extra Information

From the definitions above, one can see that

$A \cup B = B \cup A$ and$A \cap B = B \cap A$ for all sets$A$ and$B$ , but it is not necessarily the case that$A - B = B - A$ (as seen in the Sample sections above). This set theoretical fact parallels the arithmetical fact that addition is commutative but subtraction is not.