- Membership:
*x S*denotes that*x*is a member of set*S*.*x S*denotes that*x*is not a member. - Union:
*S T = { x | x S x T }*

(the set of elements*x*such that*x*is a member of set*S*or*x*is a member of set*T*(or both)). means ``or''. - Intersection:
*S T = { x | x S x T }*

(the set of elements*x*such that*x*is a member of set*S*and*x*is a member of set*T*). means ``and''. - Set Difference:
*S - T = { x | x S x T }*

(the set of elements*x*such that*x*is a member of set*S*and*x*is not a member of set*T*). - Subset:
*S T*is true if every element of*S*is an element of*T*. A*proper subset**S T*is smaller than the original set.