Operations on sets

Union of sets
The union of sets A and B is th set of all those elements which belong either to A or to B or to both A and B.

The symbol used to denote union of sets and A and B is A U B.

x Є (A U B) implies x Є A or x Є B
x does not belong to A U B implies x does not belong to A and also x does not belong to B.

Intersection of sets
The intersection of sets A and B is the set of all those elements that belong to both A and B.

The intersection of sets A and B is denoted by A ∩ B.

x Є (A ∩ B) implies x Є A and also x Є B.


Difference of sets
The difference of sets A and B, written as A-B is the set of all those elements of A which do not belong B.

It means x Є (A - B) implies x Є A or x does not belong to B.

Symmetric difference of sets
The symmetric difference of sets A and B is the set (A-B)U((B-A) and is denoted by AΔB.

AΔB = (A-B)U((B-A) = {x: x does not belong to A ∩ B).