Theory:

Disjoint set:
Two sets \(A\) and \(B\) are said to be disjoint if they do not have any element in common for two sets \(A\) and \(B\).
 
Symbolically we write \(A\cap B=\varnothing\) (where \(\varnothing\) is empty set).
 
A= {2,4,6,8},B= {10,12}.AB={2,4,6,8}{10,12}
 
Where no common elements are in the set \(A\) and \(B\).
 
\(A\) and \(B\) are disjoint.
 
So, \(A\cap B=\varnothing\)
 
Xcxc.svg
 
Important!
\(A\) and \(B\) do not have any element in common and are disjoint sets.
Overlapping sets:
Two sets \(A\) and \(B\) are said to be overlapping if they contain at least one element in common from two sets \(A\) and \(B\).
 
Symbolically we write \(A\cap B\neq \varnothing\) (where \(\varnothing\) is empty set\).
 
 A={2,4,6,8},B= {6,8,10,12}.AB={2,4,6,8}B= {6,8,10,12}
 
Where, at least one common element is in both the set \(A\) and \(B\).
 
Because \(A\) and \(B\) are overlapping.
 
So, \(A\cap B=\{6,\ 8\}\neq\varnothing\)
 
Therefore, \(A\cap B\neq\varnothing\)
 
In the Venn diagram below, the area in the blue colour represents AB.
 
Xcvcv.png