Difference of Sets
Difference of sets
Let A and B be two sets. The difference of A and B written as A – B, is the set of all those elements of A which do not belong to set B
Thus A – B={ x : x ∈ A and x ∉ B}
or A – B={ x ∈ B : x ∉ B}
Clearly, x ∈ A-B ⇔ x ∈ B and x ∉ B
In Fig (vii) the shaded region show A – B
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| Fig (vii) |
Similarly the difference B – A is the set of all those elements of B that do not belongs to set A
B – A={ x : x ∈ B and x ∉ A }
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| Fig (viii) |
In Fig (viii) shaded region represents B – A
Example
A={ 2, 3, 4, 5, 6, 7 } and B={ 3, 5, 7, 9, 11, 13}, then A – B={ 2, 4, 6} and B-A={ 9, 11, 13}