**Well-defined**

Well defined means an object or thing or element that is ”**clearly defined” or ”described**”, meaning there is no need to describe more.

**Well-defined set Example:**

- A = {1,3,5,7} here the 1,3,5,7 all are well defined. All have their own value.

This set is consist of the first four **odd numbers**. That is a well-defined set.

This set is consist of two **distinct** dishes. This is a well-defined set.

**you can also see the below examples.**

**The set of even numbers**: {2, 4, 6, 8, 10, …}**The set of prime numbers less than 10**: {2, 3, 5, 7}**The set of all vowels in the English alphabet**: {a, e, i, o, u}**The set of natural numbers less than 100**: {1, 2, 3, …, 99}**The set of days in a week**: {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}**The set of planets in the solar system**: {Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune}**The set of colors in a rainbow**: {Red, Orange, Yellow, Green, Blue, Indigo, Violet}**The set of US states starting with the letter ‘C’**: {California, Colorado, Connecticut}**The set of all positive integers**: {1, 2, 3, 4, 5, …}**The set of shapes with four sides**: {Square, Rectangle, Rhombus, Trapezoid, Parallelogram}

## Some Practical Examples of Well defined Set:

** If a Teacher says to the student to bring a set of 5 plastic chairs, the student brings plastic chairs instead of a wooden one, because the plastic chair is well defined there is no need to clarify more.**

## Counter Examples of Well-defined Set:

**All the intelligent members of the family.**

Here **intelligence** is not well defined because we can not distinguish between the intelligence of the family members. Each member is intelligent in itself.

**All the tall boys in the Class.**

Here the tall boy is not well defined because everyone in the class is different in height so we can not distinguish.

**All the good leaders of the nation.**

Here** good leaders** are not well-defined because we can not distinguish between the good leaders of a nation. Because we don’t know about the good leader.

**Not well-Defined**

Not Well defined means an object or thing or element that is ” not **clearly defined”** meaning there is a need to describe more. If the element of a set is not well defined then it is called an undefined set.

### you can see the below examples which are not well defined.

**The set of beautiful flowers**: Beauty is subjective and lacks a precise criterion for inclusion.**The set of good books**: “Good” is a subjective term and varies depending on individual opinions and tastes.**The set of successful people**: Success can be defined in numerous ways (financial, personal, professional), making it ambiguous.**The set of delicious foods**: Taste is highly subjective and varies greatly among individuals and cultures.**The set of tall buildings**: “Tall” lacks a specific height threshold and can be interpreted differently.**The set of interesting movies**: “Interesting” is subjective and varies from person to person.**The set of happy memories**: Happiness is subjective, and memories are highly personal and can’t be objectively categorized.**The set of fast cars**: “Fast” lacks a specific speed threshold and can vary depending on context.**The set of old people**: “Old” is a relative term and lacks a specific age range.**The set of important historical events**: “Importance” is subjective and can vary depending on cultural, societal, and individual perspectives.

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