Question:
Describe the following sets in Roster form:
(i) {x : x is a letter before e in the English alphabet};
(ii) {x ∈ N : x2 < 25};
(iii) {x ∈ N : x is a prime number, 10 < x < 20};
(iv) {x ∈ N : x = 2n, n ∈ N};
(v) {x ∈ R : x > x}.
(vi) {x : x is a prime number which is a divisor of 60}
(vii) {x : x is a two digit number such that the sum of its digits is 8}
(viii) The set of all letters in the word 'Trigonometry'
(ix) The set of all letters in the word 'Better'.
Solution:
Roster form:
In this form, a set is defined by listing elements, separated by commas, within braces {}.
(i) {a, b, c, d}
(ii) {1, 2, 3, 4}
(iii) {11, 13, 17, 19}
(iv) {2, 4, 6, 8, 10,...}
(v) ϕ
(vi) {2, 3, 5}
(vii) {17, 26, 35, 44, 53, 62, 71, 80}
(viii) {T, R, I, G, O, N, M, E, Y}
(ix) {B, E, T, R}