Mathematics
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}
Answer
(i) The letters in the word HUNDRED are H, U, N, D, R, E, D. The consonants among these are H, N, D, R, D. Writing each letter only once, we get H, N, D, R.
A = {H, N, D, R}, which has 4 elements.
∴ n(A) = 4.
(ii) The letters in the word DEHRADOON are D, E, H, R, A, D, O, O, N. The vowels among these are E, A, O, O. Writing each letter only once, we get E, A, O.
B = {E, A, O}, which has 3 elements.
∴ n(B) = 3.
(iii) C = {x | x ∈ W and x2 < 50}
For x = 0, x2 = 0 < 50 ✓
For x = 1, x2 = 1 < 50 ✓
For x = 2, x2 = 4 < 50 ✓
For x = 3, x2 = 9 < 50 ✓
For x = 4, x2 = 16 < 50 ✓
For x = 5, x2 = 25 < 50 ✓
For x = 6, x2 = 36 < 50 ✓
For x = 7, x2 = 49 < 50 ✓
For x = 8, x2 = 64 > 50 ✗
C = {0, 1, 2, 3, 4, 5, 6, 7}, which has 8 elements.
∴ n(C) = 8.
(iv) D = {x | x ∈ N and x < 1}
The natural numbers are 1, 2, 3, …… There is no natural number less than 1.
D = { }, which has 0 elements.
∴ n(D) = 0.
(v) The prime numbers between 8 and 30 are 11, 13, 17, 19, 23 and 29.
E = {11, 13, 17, 19, 23, 29}, which has 6 elements.
∴ n(E) = 6.
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
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}