Mathematics
Classify the following sets as empty set, finite set or infinite set:
(i) the set of all even prime numbers > 2
(ii) the set of even prime numbers
(iii) the set of prime numbers less than one crore
(iv) {all points on a line segment of length 3 cm}
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Answer
(i) The only even prime number is 2. So, there is no even prime number greater than 2.
The set = { }
Hence, it is an empty set.
(ii) The only even prime number is 2.
The set = {2}
It has only one element.
Hence, it is a finite set (having only one element).
(iii) The prime numbers less than one crore are 2, 3, 5, 7, 11, ……, and there is a definite (countable) number of them.
Hence, it is a finite set.
(iv) A line segment, however small, contains an unlimited (uncountable) number of points.
Hence, it is an infinite set.
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