Venn. Euler used diagrams like these even earlier.
The set A ∩ B consists of elements which are members of A and B and is
called the ‘intersection’ of the two sets.
The intersection of A and B
If A = {1, 2, 3, 4, 5} and B = {1, 3, 5, 7, 10, 21}, the union is A ∪ B = {1, 2,
3, 4, 5, 7, 10, 21} and the intersection is A ∩ B = {1, 3, 5}. If we regard a set A
as part of a universal set E, we can define the complement set ¬A as consisting
of those elements in E which are not in A.
The complement of A
The operations ⋂ and ⋃ on sets are analogous to × and + in algebra. Together
with the complement operation ¬, there is an ‘algebra of sets’. The Indian-born
British mathematician Augustus De Morgan, formulated laws to show how all
three operations work together. In our modern notation, De Morgan’s laws are:
¬(A ∪ B) = (¬A) ∩(¬B)
and