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SET THEORY TYPE 1 GAME
SET THEORY TYPE 1 GAME
IDENTIFY IF THE COLLECTION IS A SET OR NOT A SET
IDENTIFY IF THE COLLECTION IS A SET OR NOT A SET
Learn the below questions with the editor of Tarkashala step by step with hints
Learn the below questions with the editor of Tarkashala step by step with hints
Tutoring: Collection of difficult topics in mathematics. Is this a set?
Tutoring: Collection of difficult topics in mathematics. Is this a set?
Q. The collection of vowels in the English alphabet. Is it a set?
Q. The collection of vowels in the English alphabet. Is it a set?
HINT: Check if the collection is fixed, specific or well-defined. Because a set must be well-defined. DO VOWELS CHANGE?
HINT: Check if the collection is fixed, specific or well-defined. Because a set must be well-defined. DO VOWELS CHANGE?
A = {a, e, i, o, u} ↑ well-defined
This collection of vowels is fixed and well-defined i.e. it does not change from person to person. A set is a well-defined collection of things/entities. ∴ It is a set //
Q. The collection of the first five prime natural numbers. Is this a set?
Q. The collection of the first five prime natural numbers. Is this a set?
HINT: Check if the collection is fixed, specific or well-defined. Because a set must be well-defined. DO THE SET OF FIRST 5 PRIME NATURAL NUMBERS CHANGE?
HINT: Check if the collection is fixed, specific or well-defined. Because a set must be well-defined. DO THE SET OF FIRST 5 PRIME NATURAL NUMBERS CHANGE?
A = {2, 3, 5, 7, 11} ↑ well defined collection
This collection is well-defined and does not vary from person to person. No one can say 4 is prime, as it is false. ∴ This collection is a set // ∵ Set is a well defined collection of things/entities.
Q. The collection of all states in the Indian Union as of April 2026. Is this a set?
Q. The collection of all states in the Indian Union as of April 2026. Is this a set?
HINT: Check if the collection is fixed, specific or well-defined. Because a set must be well-defined. CAN SOME ONE SAY THAT THE COLLECTIONS OF ALL STATES OF INDIA IS NOT SPECIFIC? CAN SOMEONE SAY MAHARASHTRA IS NOT A STATE?
HINT: Check if the collection is fixed, specific or well-defined. Because a set must be well-defined. CAN SOME ONE SAY THAT THE COLLECTIONS OF ALL STATES OF INDIA IS NOT SPECIFIC? CAN SOMEONE SAY MAHARASHTRA IS NOT A STATE?
A set is a collection of things/entities that are well-defined. We know that India has 28 states. It is fixed and well-defined, as of now. ∴ This collection is a set //
Q. The collection of past presidents of India. Is it a set?
Q. The collection of past presidents of India. Is it a set?
HINT: Check if the collection is fixed, specific or well-defined. Because a set must be well-defined. CAN SOMEONE REMOVE FORMER PRESIDENT SAY APJ ABDUL LALAM FROM THE COLLECTION? IS THE COLLECTION WELL DEFINED OR NOT?
HINT: Check if the collection is fixed, specific or well-defined. Because a set must be well-defined. CAN SOMEONE REMOVE FORMER PRESIDENT SAY APJ ABDUL LALAM FROM THE COLLECTION? IS THE COLLECTION WELL DEFINED OR NOT?
We know there are a total of 15 elected presidents & 3 interim ones. Excluding the current one, we have 14 + 3 = 17 // There is no doubt, it is well-defined. ∴ It is a set // ∵ set is a well-defined collection of entities.
Q. The collection of cricketers in the world who were out for 99 runs in a test match till today. Is it a set?
Q. The collection of cricketers in the world who were out for 99 runs in a test match till today. Is it a set?
HINT: Check if the collection is fixed, specific or well-defined. Because a set must be well-defined.
HINT: Check if the collection is fixed, specific or well-defined. Because a set must be well-defined.
We are sure that the number of such cricketers is well-counted and is well-defined. ∵ A set is well-defined collection ∴ This collection is also well-defined i.e. a set //
Q. The collection of good cricket players of India. Is it a set?
Q. The collection of good cricket players of India. Is it a set?
HINT: Check if the collection is fixed, specific or well-defined. Because a set must be well-defined. IS THE WORD GOOD WELL DEFINED?
HINT: Check if the collection is fixed, specific or well-defined. Because a set must be well-defined. IS THE WORD GOOD WELL DEFINED?
Who is good? ↑ To one person, Dhoni is good, to another, Virat is better.
The word "good" is not well-defined. It varies from person to person. ∵ A set must be a well-defined collection. ∴ This collection is not a set //
Q. Collection of all natural numbers less than 50. Is it a set?
Q. Collection of all natural numbers less than 50. Is it a set?
HINT: Check if the collection is fixed, specific or well-defined. Because a set must be well-defined. DOES THIS COLLECTION INCLUDE OR EXCLUDE 50? WHERE DO NATURAL NUMBERS START?
HINT: Check if the collection is fixed, specific or well-defined. Because a set must be well-defined. DOES THIS COLLECTION INCLUDE OR EXCLUDE 50? WHERE DO NATURAL NUMBERS START?
A = {1, 2, 3, . . . . 49} ↑ This is a well-defined collection, there can be only these numbers in this collection 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 and no OTHER number. ∴ It is a set //
Q. The collection of good hockey players in India. Is it a set?
Q. The collection of good hockey players in India. Is it a set?
HINT: Check if the collection is fixed, specific or well-defined. Because a set must be well-defined.
HINT: Check if the collection is fixed, specific or well-defined. Because a set must be well-defined.
What is "good"? It is not well defined. One player may be good according to a person A, another is good according to a person B. So, this collection is not well defined. => Not a set // ∵ A set is a well-defined collection of entities.
Q. The collection of all girls in your class. Is it a set?
Q. The collection of all girls in your class. Is it a set?
HINT: Check if the collection is fixed, specific or well-defined. Because a set must be well-defined
HINT: Check if the collection is fixed, specific or well-defined. Because a set must be well-defined
Yes, it is a set. We can count the number of girls in a particular class. It is well-defined. A set is a well-defined collection of things/entities.
Q. The collection of the most talented writers of India. It is a set. True or False?
Q. The collection of the most talented writers of India. It is a set. True or False?
HINT: Check if the collection is fixed, specific or well-defined. Because a set must be well-defined. IS THE WORD TALENTED WELL DEFINED?
HINT: Check if the collection is fixed, specific or well-defined. Because a set must be well-defined. IS THE WORD TALENTED WELL DEFINED?
For a mother the most talented writer may be her child. For another it may be Premchand. For another younger person it may be Chetan Bhagat. => "most talented" is vague i.e. not well defined. ∴ It is not a set. ∴ False //
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