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Section 1

Introduction

Which of the following are sets ? Justify your answer.(i) The collection of all the months of a year beginning with the letter J.(ii) 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 100 .(vi) A collection of novels written by the writer Munshi Prem Chand.(vii) The collection of all even integers. (viii) The collection of questions in this Chapter.(ix) A collection of most dangerous animals of the world.

Let $\mathrm{A}=\{1,2,3,4,5,6\}$. Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces:(i) $5 \ldots$ A(ii) $8 \ldots$ A(iii) $0 . \ldots \mathrm{A}$(iv) $4 \ldots$ A(v) 2....A(vi) $10 \ldots$ A

Write the following sets in roster form:(i) $\mathrm{A}=\{x: x$ is an integer and $-3 \leq x<7\}$(ii) $\mathrm{B}=\{x: x$ is a natural number less than 6$\}$(iii) $\mathrm{C}=\{x: x$ is a two-digit natural number such that the sum of its digits is 8$\}$(iv) $\mathrm{D}=\{x: x$ is a prime number which is divisor of 60$\}$(v) $\mathrm{E}=$ The set of all letters in the word TRIGONOMETRY(vi) $\mathrm{F}=$ The set of all letters in the word BETTER

Write the following sets in the set-builder form:(i) $(3,6,9,12\}$(ii) $\{2,4,8,16,32\}$(iii) $\{5,25,125,625\}$(iv) $\{2,4,6, \ldots\}$(v) $\{1,4,9, \ldots, 100\}$

List all the elements of the following sets:(i) $\mathrm{A}=\{x: x$ is an odd natural number $\}$(ii) $\mathrm{B}=\left\{x: x\right.$ is an integer, $\left.-\frac{1}{2}<x<\frac{9}{2}\right\}$(iii) $\mathrm{C}=\left\{x: x\right.$ is an integer, $\left.x^{2} \leq 4\right\}$(iv) $\mathrm{D}=\{x: x$ is a letter in the word "LOYAL" $\}$(v) $\mathrm{E}=\{x: x$ is a month of a year not having 31 days \}(vi) $\mathrm{F}=\{x: x$ is a consonant in the English alphabet which precedes $k\}$.

Match each of the set on the left in the roster form with the same set on the right described in set-builder form:(i) $\{1,2,3,6\}$(a) $\{x: x$ is a prime number and a divisor of 6$\}$(ii) $\{2,3\}$(b) $\{x: x$ is an odd natural number less than 10$\}$(iii) $\{\mathrm{M}, \mathrm{A}, \mathrm{T}, \mathrm{H}, \mathrm{E}, \mathrm{I}, \mathrm{C}, \mathrm{S}\}$(c) $\{x: x$ is natural number and divisor of 6$\}$(iv) $\{1,3,5,7,9\}$(d) $\{x: x$ is a letter of the word MATHEMATICS\}