Double Math

Examples of well-defined sets


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.

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

well-defined set

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.

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

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