Question 3 of 47beginner🔧 ApplyShort Answer4 marks

Write the following sets in roster form:

(i)

A = {x : x is an integer and –3 ≤\leq x < 7}

Answer

A = {-3, -2, -1, 0, 1, 2, 3, 4, 5, 6}

(ii)

B = {x : x is a natural number less than 6}

Answer

B = {1, 2, 3, 4, 5}

(iii)

C = {x : x is a two-digit natural number such that the sum of its digits is 8}

Answer

C = {17, 26, 35, 44, 53, 62, 71, 80}

(iv)

D = {x : x is a prime number which is divisor of 60}

Answer

D = {2, 3, 5}

(v)

E = The set of all letters in the word TRIGONOMETRY

Answer

E = {T, R, I, G, O, N, M, E, Y}

(vi)

F = The set of all letters in the word BETTER

Answer

F = {B, E, T, R}

Explanation

This question tests the understanding of roster form representation of sets. As per the textbook, in roster form, all elements are listed separated by commas within braces {}. Key points to remember: (1) Order of elements is immaterial, (2) Elements are not repeated - all elements are distinct. For part (i), integers from -3 to 6 are listed. For part (ii), natural numbers start from 1, so numbers 1-5 are included. For part (iii), all two-digit numbers whose digits sum to 8 are found systematically. For part (iv), prime divisors of 60 are identified by factorizing 60 = 2² × 3×53 \times 5. For parts (v) and (vi), letters are listed without repetition as per the note in the textbook.