Difference of two set definition”The set of all element of A which does not belong to B”. The difference of two set A and B is denoted by mathematical symbol A ⁄ B OR A – B
Set builder form :
A – B = { x ⁄ x ∈ A ∧ x ∉ B }
A – B read A negative B
x ∈ A ∧ x ∉ B Read x is a part of A ,, X is not a part of B.
similarly,
B – A = { x ⁄ x ∈ B ∧ x ∉ A }
B – A read B negative A
x ∈ B ∧ x ∉ A Read x is a part of B ,, X is not a part of A.
A and B are disjoint sets:
A- B means all element of A
B – A means all element of B
EXAMPLE:
A = { 1,2,8 } . B = { 4, 9 }
A – B = { 1, 2, 8}
B – A = { 4 ,9 }
A and B are overlapping sets:
A- B means all element of A which are not in B.
B – A means all element of B which are not in A.
EXAMPLE:
A = { 1,2,8 } . B = {2, 4, 9 }
A – B = { 1, 8}
B – A = { 4 ,9 }
A is subset of B:
A- B means all element of A which are not in B.
B – A means all element of B which are not in A.
EXAMPLE:
A = { 1,2,8 } . B = {2, 4, 9,10 }
A – B = { 1, 8}
B – A = { 4 ,9,10 }
B is subset of A:
A- B means all element of A which are not in B.
B – A means all element of B which are not in A.
EXAMPLE:
A = { 7,9, 11, 12 } . B = {7,9 }
A – B = { 11, 12 }
B – A = { }
Keep in mind:
A – B ≠ B – A
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