Question 7 of 47beginner💡 UnderstandShort Answer2 marks

Which of the following sets are finite or infinite

(i)

The set of months of a year

Answer

Finite

(ii)

{1, 2, 3, ...}

Answer

Infinite

(iii)

{1, 2, 3, ..., 99, 100}

Answer

Finite

(iv)

The set of positive integers greater than 100

Answer

Infinite

(v)

The set of prime numbers less than 99

Answer

Finite

Explanation

The textbook defines a finite set as one which is empty or consists of a definite number of elements, while an infinite set has elements that are not finite. For part (i), months of a year are exactly 12 in number - a definite count. Part (ii) represents the set of natural numbers {1, 2, 3, ...} which the context explicitly states is infinite. Part (iii) has elements from 1 to 100, giving exactly 100 elements - a definite number. Part (iv) has positive integers starting from 101 onwards with no upper limit, hence infinite. Part (v) has prime numbers less than 99, which are countable and definite in number, making it finite.