Properties Of Set Operations Examples

2 cs 441 discrete mathematics for cs m.

Properties of set operations examples. A a u b b u a set union is commutative b a n b b n a set intersection is commutative. Vowels in the english alphabet v a e i o u first seven prime numbers. Let a 3 7 11 and b x. Then since a a and a b by 7 a a a b.

Since a a a by 3 a a b. Equalities involving set operations intersection of sets subset relations proofs of equalities. Intersection property of the empty set. The intersection property of the empty set says that any set intersected with the empty set gives the empty set.

These objects are sometimes called elements or members of the set. In this case it was factoring out a 6. 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. Any set of sets closed under the set theoretic operations forms a.

Here four basic operations are introduced and their properties are discussed. 6 2x 3 12x 18 this example was taking the number through the parentheses. For example suppose that committee a consisting of the 5 members jones blanshard nelson smith and hixon meets with committee b. Here are some useful rules and definitions for working with sets.

For example a set f can be specified as follows. The distribution property means to taking a number or a variable through the parentheses or factoring something out. A set is a unordered collection of objects. When two or more sets are combined together to form another set under some given conditions then operations on sets are carried out.

Hauskrecht set definition. Let x be an arbitrary element in the. 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. In set builder notation the set is specified as a selection from a larger set determined by a condition involving the elements.

I commutative property. X is a natural number less than 0. 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. A a.

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. 6x 18 6 x 3 this example shows using distribution by factoring something out. Cantor s naive definition examples. Properties of set operation subjects to be learned.

The symbol is employed to denote the union of two sets. The union of sets a and b denoted by a b is the set defined as. . X 2 3 5 7 11 13 17.