Maths Practical Application of Set Problems. If U is the universal set and A and B are two intersecting subsets, the diagram below shows how to represent the Set A and B in a diagram.

Region 1 represents the elements that are in set A but not in set B.
In set notation, this is expressed as $A \setminus B$ or $A \cap B'$.

Region 2 represents the elements that are common to both set A and set B. This is the intersection of A and B.
In set notation, this is expressed as $A \cap B$.

Region 3 represents the elements that are in set B but not in set A.
In set notation, this is expressed as $B \setminus A$ or $B \cap A'$.

Region 4 represents the elements that are neither in set A nor in set B, but are within the universal set U. This is the complement of the union of A and B.
In set notation, this is expressed as $(A \cup B)'$ or $U \setminus (A \cup B)$.