Properties Of Set Operations Examples
The algebra of sets defines the properties and laws of sets the set theoretic operations of union intersection and complementation and the relations of set equality and set inclusion it also provides systematic procedures for evaluating expressions and performing calculations involving these operations and relations.
Properties of set operations examples. In this notation the vertical bar means such that and the description can be interpreted as f is the set of all numbers n such that n is an integer in the range from 0 to 19 inclusive. 2 cs 441 discrete mathematics for cs m. Vowels in the english alphabet v a e i o u first seven prime numbers. Any set of sets closed under the set theoretic operations forms a.
Intersection property of the empty set. Here are some useful rules and definitions for working with sets. For example suppose that committee a consisting of the 5 members jones blanshard nelson smith and hixon meets with committee b. Complement of set ordered pair ordered n tuple equality of ordered n tuples cartesian product of sets contents sets can be combined in a number of different ways to produce another set.
6 2x 3 12x 18 this example was taking the number through the parentheses. In set builder notation the set is specified as a selection from a larger set determined by a condition involving the elements. The intersection property of the empty set says that any set intersected with the empty set gives the empty set. X 2 3 5 7 11 13 17.
6x 18 6 x 3 this example shows using distribution by factoring something out. For example a set f can be specified as follows. When two or more sets are combined together to form another set under some given conditions then operations on sets are carried out. For example b can be proven as follows.
. A a u b b u a set union is commutative b a n b b n a set intersection is commutative. First by 15 a b a. Let a 3 7 11 and b x.
X is a natural number less than 0. I commutative property. The symbol is employed to denote the union of two sets. Hauskrecht set definition.
A set is a unordered collection of objects. Properties of set operation subjects to be learned. Here four basic operations are introduced and their properties are discussed. In this case it was factoring out a 6.
Then since a a and a b by 7 a a a b. Let x be an arbitrary element in the. These objects are sometimes called elements or members of the set. The distribution property means to taking a number or a variable through the parentheses or factoring something out.
Since a a a by 3 a a b. Cantor s naive definition examples. Thus the set a b read a union b or the union of a and b is defined as the set that consists of all elements belonging to either set a or set b or both. The union of sets a and b denoted by a b is the set defined as.