Which of the following sets are finite or infinite

(i) The set of months of a year

(ii) {1, 2, 3 …}

(iii) {1, 2, 3 … 99, 100}

(iv) The set of positive integers greater than 100

(v) The set of prime numbers less than 99

Asked by Pragya Singh | 11 months ago |  72

1 Answer

Solution :-

(i) Given that,

The sets of months of a year

To find if the set is finite or infinite

A set which is empty or consists of a definite number of elements is called finite

otherwise the set is called infinite.

A year has twelve months which has defined number of elements

The set of months of a year is finite.

 

(ii) Given that,

{1, 2, 3 …}

To find if the set is finite or infinite

A set which is empty or consists of a definite number of elements is called finite

otherwise the set is called infinite.

The set {1, 2, 3 …} consists of an infinite number of natural numbers.

 

(iii) Given that,

{1, 2, 3 … 99, 100}

To find if the set is finite or infinite

A set which is empty or consists of a definite number of elements is called finite

otherwise the set is called infinite.

This set contains the elements from 1 to 100which are finite in number.

The set {1, 2, 3 … 99, 100} is finite.

 

(iv) Given that,

The set of positive integers greater than 100

To find if the set is finite or infinite

A set which is empty or consists of a definite number of elements is called finite otherwise the set is called infinite.

The positive integers which are greater than 100 are infinite in number.

The set of positive integers greater than 100 is infinite.

 

 

(v) Given that,

The set of prime numbers less than 99

To find if the set is finite or infinite

A set which is empty or consists of a definite number of elements is called finite

otherwise the set is called infinite.

The prime numbers less than 99 are finite in number.

The set of prime numbers less than 99 is finite.

Answered by Abhisek | 11 months ago

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