Mathematics
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
Sets
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Answer
(i) The even whole numbers less than 50 are 0, 2, 4, 6, ……, 48.
Roster form: A = {0, 2, 4, 6, ……, 48}
Set builder form: A = {x : x ∈ W and x is an even number < 50}
(ii) The two digit numbers are 10, 11, 12, ……, 99. Out of these, the perfect squares are:
42 = 16, 52 = 25, 62 = 36, 72 = 49, 82 = 64 and 92 = 81
Roster form: B = {16, 25, 36, 49, 64, 81}
Set builder form: B = {x : x is a perfect square and two digit number}
(iii) The letters in the word MUSSOORIE are M, U, S, S, O, O, R, I, E. Writing each letter only once, we get M, U, S, O, R, I, E.
Roster form: {M, U, S, O, R, I, E}
Set builder form: {x : x is a letter in the word MUSSOORIE}
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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}
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}
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}