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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  A and x  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

In case B  A, then A - B is the region which lies inside A but outside B. as shown in Figure 3 
Lastly, if A  B, then A - B = φ as shown in Figure 4.
 

Fig. 3

Fig. 4

Example
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 = φ ; B = {x : x  N}

Solution
A - B = φ

Example
Find A - B for the following:
A = {x : x  N}; B = {x : x  N}

Solution
A - B = φ

Example
Find A - B for the following:
A = {x  x  N}; B = {x  x is odd}

Solution
A - B = {x : x  N and x is even}




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