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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