Question

Which of the following is not set?
A.The collection of months in a year.
B.The collection of some months in a year.
C.The collection of first ten prime numbers.
D.The collection of days in a week.

Answer 1

Hint: We will use the definition of a set to solve this question. For every given option, we will find the elements of the set and will verify if the collection of the given information (elements) forms a set or not.

Complete step-by-step answer:
We are given 4 options and we need to find out the one which is not a set.
Definition of a set: In mathematics, a set is a well – defined collection of various things. Or, we can say that any collection of objects, mathematical or not, if well defined, is called a set and every member of the set is known as an element.
A set is basically an organized representation of the elements enclosed in curly brackets.
Considering options to verify if they form a set or not:
Option (A): The collection of months in a year
The elements of this set will be: January, February, March, April, May, June, July, August, September, October, November and December.
Hence, the set will be finite and well defined since all the elements of this set are definite. The set can be represented as:
$S=\left\{\text{January, February, March, April, May, June, July, August, September, October, November, December}\right\}$Therefore, option (A) constitutes a set.
Option (B): The collection of some months in a year
In this option, we are not specified with which months of the year are there in the set. Hence, this option has no definite information and therefore, it is impossible to find the elements and hence the set.
Therefore, option (B) does not form a set.
Option (C): The collection of first ten prime numbers
The elements of this set are: 1, 2, 3, 5, 7, 11, 13, 17, 23, and 29.
They can be represented in form of a set as: $S=\left\{1,2,3,5,7,11,13,17,23,29\right\}$
Hence, option (C) also forms a set as the set S is defined.
Option (D): The collection of days in a week
The elements of this set are: Monday, Tuesday, Wednesday, Thursday, Friday and Saturday.
The set will be:$S=\left\{\text{Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}\right\}$
Hence, option (D) constitutes a set being its elements finite and well – defined.
Hence option B is the correct answer.

Note: In such questions, you should solve the questions by taking account of the definition of the concept used such as we have used the definition of set to solve this question. The things which are not certain or well – defined, they cannot form a set as a set needs to be definite such as all the birds in the sky, all the notes in a bank, members of Indian basketball team are such examples which cannot constitute a set since all of them are indefinite.