Question:
Which of the following is a set?
Which of the following is a set?
Updated On: Jul 7, 2022
- The collection of all the months of a year beginning with the letter $J$
- The collection of ten most talented writers of India
- A team of eleven best cricketers of the world
- A collection of most dangerous animals of the world
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The Correct Option is A
Solution and Explanation
(a) We are sure that members of this collection are January, June and July. So, this collection is well defined and hence, it is a set.
(b) A writer may be most talented for one person and may not be for other. Therefore, it cannot be said that which writer will be talented. So, this collection is not well defined. Hence, it is not a set.
(c) A batsman may be best for one person and may not be so for other. Therefore, it cannot be said that which batsman will be the best.
(d) The term most dangerous is not a clear term. An animal may be most dangerous to one person and may not be for the other. So, it is not well defined, hence it is not a set.
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Concepts Used:
Sets
Set is the collection of well defined objects. Sets are represented by capital letters, eg. A={}. Sets are composed of elements which could be numbers, letters, shapes, etc.
Example of set: Set of vowels A={a,e,i,o,u}
Representation of Sets
There are three basic notation or representation of sets are as follows:
Statement Form: The statement representation describes a statement to show what are the elements of a set.
- For example, Set A is the list of the first five odd numbers.
Roster Form: The form in which elements are listed in set. Elements in the set is seperatrd by comma and enclosed within the curly braces.
- For example represent the set of vowels in roster form.
A={a,e,i,o,u}
Set Builder Form:
- The set builder representation has a certain rule or a statement that specifically describes the common feature of all the elements of a set.
- The set builder form uses a vertical bar in its representation, with a text describing the character of the elements of the set.
- For example, A = { k | k is an even number, k ≤ 20}. The statement says, all the elements of set A are even numbers that are less than or equal to 20.
- Sometimes a ":" is used in the place of the "|".