Recognizing Descriptive Notation — Which set is defined descriptively?

Examples A and C define the set elements by enumeration. B uses a rule: it contains every x that is a prime number and less than 20, so this is descriptive notation.

Descriptive Set Notation

Cardinality of Sets Applications of Sets

A set can be defined in two ways: by enumeration or by a property. Descriptive (property-based) notation means specifying the condition that an element must satisfy to belong to the set.

Enumerative Notation

Here, we simply list the elements in curly braces. Example: A = {1,2,3,4}.

Descriptive Notation

The set is defined by a rule or property. Example: B = {x | x is an even number and x < 10}. This means B contains all even numbers less than 10.

Everyday Examples

C = {x | x is a fruit that is red} → for example: {apple, cherry, strawberry}.
D = {x | x is a season in which it often rains} → for example: {spring, autumn}.
E = {x | x is a day of the week that is a workday} → {Monday, Tuesday, Wednesday, Thursday, Friday}.

Summary

Enumerative notation is useful when there are few elements. However, if the set is large or infinite, descriptive notation is more appropriate because it can be described briefly with a rule.

Practice Exercise

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