Let us examine the defining set of intersection :

We consider an arbitrary element, say “x”, of the difference set. Then, we interpret the conditional meaning as :

The conditional statement is true in opposite direction as well. Hence,

We can summarize two statements with two ways arrow as :

**Composition of a set**

From Venn’s diagram, we observe that if we derive union of (

Difference of two sets |
---|

and

**Difference of sets is not commutative **

The positions of sets about minus operator affect the result. It is clear from the figure above, where “A-B” and “B-A” represent different regions on Venn’s diagram. As such, the difference of sets is not commutative. Let us consider the example used earlier, where :

Then,

and

Clearly,

**Symmetric difference**

From the Venn’s diagram, we can see that union of two sets is equal to three distinct regions. Alternatively, we can say that the region represented by the union of two sets is equal to the sum of the regions representing three “disjoint” sets (i) difference set A-B (ii) intersection set "

Difference of two sets |
---|

We use the term “symmetric set” for combining two differences as marked on Venn’s diagram. It is denoted as “