Difference of Sets
Let A and B be two sets. We define the difference between A and B to be the set of all elements which belong to A but not to B. This set is denoted by A  B. That is, A  B = {x  x âˆˆ A and x âˆ‰ B}.In Venn diagram A  B corresponds to the region consisting of all the points in A but not contained in B as shown in Figure 1.
If A and B are disjoint, then A  B is whole of A as shown in Figure 2.



Fig.1 
Fig.2 
Lastly, if A âŠ‚ B, then A  B = Ï† as shown in Figure 4.



Fig. 3 
Fig. 4 
Find A  B for the following:
A = {1, 3, 5, 7}; B = {5, 9, 11}
Solution
Given : A = {1, 3, 5, 7}; B = {5, 9, 11}
Therefore A  B = {1, 3, 7,}
{1, 3, 7,}
Example
Find A  B for the following:
A = {2, 5, 7, 8}; B = {3, 8, 11}
Solution
A  B = {2, 5, 7}
Example
Find A  B for the following:
A = {6, 11, 15, 17}; B = {9, 8, 20}
Solution
A  B = {6, 11, 15, 17}
Example
Find A  B for the following:
A = Ï† ; B = {x : x âˆˆ N}
Solution
A  B = Ï†
Example
Find A  B for the following:
A = {x : x âˆˆ N}; B = {x : x âˆˆ N}
Solution
A  B = Ï†
Example
Find A  B for the following:
A = {x âˆ x âˆˆ N}; B = {x âˆ x is odd}
Solution
A  B = {x : x âˆˆ N and x is even}