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Question

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

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Solution

(i) The set of months of a year is a finite set as it is containing 12 elements (i.e.,12 months).

(ii) Given set {1,2,3,...} is an infinite set, because it has infinite number of natural numbers.

(iii) Since the numbers from 1 to 100 are finite. So given set is a finite set.

(iv) Since the positive integers which are greater than 100 are infinite. So given set is an infinite set.

(v) Since the prime numbers which are less than 99 are countable. So given set is a finite set.

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