Venn Diagram & Set Operations

The set of all elements in the universal set that are not in set A is called the _____of set​ A, and is symbolized by_____.

complement

A'

The formula for the cardinal number of elements in set A or set B is

n left parenthesis Upper A union Upper B right parenthesisequals​________.

n(A) + n(B) - (nA n B)

Describe what is meant by a universal set. Provide an example.

The universal set is the set that contains all the elements being considered in a given discussion or problem. For​ example, if a discussion is on the color of U.S. cars by​ model, the universal set might be models of all U.S. cars.

What is a Venn diagram and how is it​ used?

A Venn diagram is a visual representation of the relationship among sets. It is used to provide precise ways of​ organizing, classifying, and describing a wide variety of data.

Assume

Anot equalsB.

Draw a Venn diagram that correctly illustrates the relationship between the two sets.

A

intersect

BequalsA

In order to perform set operations such as left parenthesis Upper A union Upper B right parenthesis intersect left parenthesis Upper A union Upper C right parenthesis​,begin by performing any set operations

inside parenthesis

Determine whether the statement is true or false. If the statement is​ false, make the necessary​ change(s) to produce a true statement.

Inductive reasoning is used to prove the equality of sets.

The statement is false. A similar statement that is true is​ "Deductive reasoning is used to prove the equality of​ sets.

It can be proved that left parenthesis Upper A intersect Upper B right parenthesis prime equals Upper A prime union Upper B prime​,so this means that the complement of the intersection of two sets is the union of the complement of those sets.

The statement is true because a theorem is always true and left parenthesis Upper A intersect Upper B right parenthesis prime equals Upper A prime union Upper B prime means that the complement of the intersection of two sets is the union of the complement of those sets.