Dr. J introduces set operations including union, intersection, set difference and set complement. The union of two sets contains all the elements in either set. The intersection of two sets contains the elements that are in both sets. The set difference of A minus B contains all the elements in A that are not in set B. When working with sets, there is often a universal set S that is the union of all possible sets. The complement of a set A (relative to the universal set S) contains all the elements in S that are not in A. Thus the complement is a set difference, but typically the universal set is implicit.
The video also discusses many properties of these set operations including the identity property of unions and intersections, commutative and associative property of unions and intersections, and the distributive property of unions over intersections and intersections over unions. Additional properties typically referred to as De Morgan’s laws are also introduced.