Properties Of Set Operations Examples

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.

Properties of set operations examples. Cantor s naive definition examples. First by 15 a b a. Vowels in the english alphabet v a e i o u first seven prime numbers. The following are the important properties of set operations.

. For example suppose that committee a consisting of the 5 members jones blanshard nelson smith and hixon meets with committee b. Properties of set operation subjects to be learned. The intersection property of the empty set says that any set intersected with the empty set gives the empty set.

Then since a a and a b by 7 a a a b. These objects are sometimes called elements or members of the set. Let a 3 7 11 and b x. I commutative property.

In set builder notation the set is specified as a selection from a larger set determined by a condition involving the elements. The distribution property means to taking a number or a variable through the parentheses or factoring something out. 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. Here are some useful rules and definitions for working with sets.

6x 18 6 x 3 this example shows using distribution by factoring something out. Let x be an arbitrary element in the. 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. Hauskrecht set definition.

In this case it was factoring out a 6. Any set of sets closed under the set theoretic operations forms a. 6 2x 3 12x 18 this example was taking the number through the parentheses. X is a natural number less than 0.

Intersection property of the empty set. Since a a a by 3 a a b. 2 cs 441 discrete mathematics for cs m. A a u b b u a set union is commutative b a n b b n a set intersection is commutative.

X 2 3 5 7 11 13 17. 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. Here four basic operations are introduced and their properties are discussed. When two or more sets are combined together to form another set under some given conditions then operations on sets are carried out.

Equalities involving set operations intersection of sets subset relations proofs of equalities. For example a set f can be specified as follows. A a. The union of sets a and b denoted by a b is the set defined as.