Difference of set - Practice Questions & MCQ

The difference between the sets $A$ and $B$ in this order is the set of elements that belong to $A$ but not to B .

Symbolically, we write A - B and read as "A minus B".
For example, If $A=\{1,2,3,4\}$ and $B=\{4,5,6,8\}$,
Then, $A-B=\{1,2,3\}$ and $B-A=\{5,6,8\}$

The sets $A-B, A \cap B$ and $B-A$ are mutually disjoint sets, i.e., the intersection of any two of these sets is the null set as shown in figured

Properties of Difference of Sets

1. In general $A$ - $B$ does not equal $B$ - $A$
2. $\mathrm{A}-\mathrm{A}=\phi$
3. $\mathrm{A}-\phi=\mathrm{A}$
4. $\mathrm{A}-\mathrm{U}=\phi$
5. If $A$ is a subset of $B$, then $A-B=\phi$

Symmetric Difference of Sets ( $A \Delta B$ )
The symmetric difference of two sets $A$ and $B$ is defined as

$
A \Delta B=(A-B) \cup(B-A)
$

Venn Diagram

Clearly,  A Δ B also equals ( A ∪ B) - ( A ∩ B )