Q7. Which of these are sets? (i) The collection of all boys in your class; (ii) a team of eleven best cricket batsmen of the world; (iii) the collection of all even integers; (iv) the collection of questions in this chapter; (v) a collection of novels written by the writer Munshi Prem Chand (NCERT Exercise 1.1, Q1 (iii), (iv), (vi), (vii), (viii)).
(i), (iii), (iv) and (v) are sets: membership can be checked. (ii) is not, because “best” is a matter of opinion.
Q8. Write in roster form: F = {x : x is a consonant in the English alphabet which precedes k} (NCERT Exercise 1.1, Q5 (vi)).
The letters before k are a to j; removing the vowels a, e and i leaves {b, c, d, f, g, h, j}.
Q9. List the elements of B = {x : x is an integer, −1/2 < x < 9/2} (NCERT Exercise 1.1, Q5 (ii)).
−1/2 = −0.5 and 9/2 = 4.5, so the integers are 0, 1, 2, 3 and 4: B = {0, 1, 2, 3, 4}.
Q10. Write {1, 8, 27, 64, 125} in set-builder form and say how many elements it has.
{x : x = n3, n ∈ N and 1 ≤ n ≤ 5}; five elements.
Q11. Write in roster form the set of letters of the word MISSISSIPPI, and say how many elements it has.
{M, I, S, P}: four elements. Each repeated letter is written once.
Q12. Write the set of all natural numbers x such that 2x + 1 ≤ 9 in roster form.
2x ≤ 8, so x ≤ 4: {1, 2, 3, 4}.