# Operations on Sets theory

## Union of sets

Union of sets Let A and B be any two sets. The union of A and B is the set which consists of all the elements of A and all the elements of B, the common elements being taken only once. The symbol ‘∪’ is used to denote the union. Symbolically, we write A ∪ B and usually read as ‘A union B’

Example Let A = { 2, 4, 6, 8} and B = { 6, 8, 10, 12}. Find A ∪ B

Solution We have A ∪ B = { 2, 4, 6, 8, 10, 12}

## Intersection of sets

Intersection of sets The intersection of sets A and B is the set of all elements which are common to both A and B. The symbol ‘∩’ is used to denote the intersection. The intersection of two sets A and B is the set of all those elements which belong to both A and B. Symbolically, we write A ∩ B = {x : x ∈ A and x ∈ B}

Example Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and B = { 2, 3, 5, 7 }. Find A ∩ B and
hence show that A ∩ B = B

Solution We have A ∩ B = { 2, 3, 5, 7 } = B. We
note that B ⊂ A and that A ∩ B = B

## Difference of sets

Difference of sets The difference of the sets A and B in this order is the set of elements which belong to A but not to B. Symbolically, we write A – B and read as “ A minus B”

Example Let A = { 1, 2, 3, 4, 5, 6}, B = { 2, 4, 6, 8 }. Find A – B and B – A

Solution We have, A – B = { 1, 3, 5 }, since the elements 1, 3, 5 belong to A but
not to B and B – A = { 8 }, since the element 8 belongs to B and not to A.
We note that A – B ≠ B – A