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}
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.
Related Questions
Write the following sets in the roster form:
(i) A = {x | x is a month of a year having 30 days}
(ii) B = {x | x = 2n, n ∈ W and n < 5}
(iii) C = {x | x ∈ N and x2 < 40}
(iv) D = {all letters in the word PERMISSION}
(v) E = {x : x ∈ I and x2 < 10}
(vi) F = {x : x ∈ N, 15 < x < 50 and x is divisible by 6}
(vii) the set of whole numbers which are greater than 14 and divisible by 7
(viii) the set of signs of four fundamental operations of arithmetic.
Write the following sets in set builder form:
(i) A = {2, 3, 5, 7, 11, 13, 17, 19}
(ii) B = {all months of a year}
(iii) C = {Monday, Tuesday, Wednesday}
Write the following sets in roster form and also in set builder form:
(i) A = {even whole numbers which are less than 50}
(ii) B = {two digit numbers which are perfect square}
(iii) the set of letters in the word MUSSOORIE
Find the cardinal number of the following sets:
(i) A = {x | x is a consonant in the word HUNDRED}
(ii) B = {x | x is a vowel in the word DEHRADOON}
(iii) C = {x | x ∈ W and x2 < 50}
(iv) D = {x | x ∈ N and x < 1}
(v) E = {x | x is a prime number between 8 and 30}