6 - Regular Languages GapFill

Set notation, as well as its attendant terms, is a language in its own right, and it's important to get to grips with the basics of it, since sets in computer science are ubiquitous. The number of elements in a set is known as the set's  capacityproportioncardinalitymagnitude, i.e. a value of '7' in this context means that a set contains seven elements.

The  ConstantCommonCartesianCoordinate product of two sets outputs all combinations of the two sets in the form of  bi-partstupletscoordinatesordered pairs. For example, this operation performed on the sets 1, 2 and 3, 4 would produce (1,3), (1,4), (2,3), (2,4). Note that this operation can be performed upon more than two sets, as well as on a single set. Any set whose members can all be found within another set can be described as a  semi-setsubordinate setsummed setsubset of that other set.

The  intersectionuniondifferencemembership of two sets produces an output containing only elements that are present in both of the component sets. The  unionmembershipdifferenceintersection of two sets outputs all members of both sets, with any duplicate values removed (since no set can contain the same value twice). Finally, the  membershipintersectionuniondifference applied to sets A and B would output all members of set A except for those that also belong to set B. This operation performed on sets B and A would have a different outcome from the same operation performed on sets A and B.