{P, R, I, N, C, A, L} (a) { x : x is a positive integer and is a divisor of } { } (b) { x : x is an integer and x – = } (iii) { , , , , , } (c) { x : x is an integer and x + = } (iv) { , – } (d) { x : x is a letter of the word PRINCIPAL} Solution Since in (d), there are letters in the word PRINCIPAL and two letters P and I are repeated, so (i) matches (d). Similarly, (ii) matches (c) as x + = implies x = . Also, , , , , , are all divisors of and so (iii) matches (a). Finally, x – = implies x = , – and so (iv) matches (b).
EXERCISE . . Which of the following are sets ? Justify your answer.
The collection of all the months of a year beginning with the letter J. The collection of ten most talented writers of India. (iii) A team of eleven best-cricket batsmen of the world. (iv) The collection of all boys in your class.
(v) The collection of all natural numbers less than . (vi) A collection of novels written by the writer Munshi Prem Chand. (vii) The collection of all even integers. SETS (viii) The collection of questions in this Chapter.
(ix) A collection of most dangerous animals of the world. . Let A = { , , , , , }. Insert the appropriate symbol ∈ or ∉ in the blank spaces: .
. .A . Write the following sets in roster form: A = { x : x is an integer and – ≤ x < } B = { x : x is a natural number less than } (iii) C = { x : x is a two-digit natural number such that the sum of