Question 1: Describe the following sets in Roster form:

(i) $\{x : x$ is a letter before $e$ in the English alphabet $\}$

(ii) $\{x \in N : x^2 < 25\}$

(iii) $\{ x \in N : x$ is a prime number, $10 < x < 20\}$

(vi) $\{ x \in N : x =2n, n \in N \}$

(v) $\{ x \in R:x>x\}$

(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’

(i) $\{ a, b, c, d \}$

(ii) $\{ 1, 2, 3, 4 \}$

(iii) $\{ 11, 13, 17, 19 \}$

(vi) $\{ 2, 4, 6, 8, 10, \cdots\}$

(v) $\phi$

(vi) $\{ 2, 3, 5 \}$

(vii) $\{ 17, 26, 35, 44, 53, 62, 71, 80 \}$

(viii) $\{ T, R, I, G, O, N, M, E, Y \}$

(ix) $\{B, E, T, R \}$

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Question 2: Describe the following sets in set-builder form:

(i) $A =\{1,2,3, 4,5, 6\}$

(ii) $B = \{ 1,$ $\frac{1}{2}$ $,$ $\frac{1}{3}$ $,$ $\frac{1}{4}$ $,$ $\frac{1}{5}$ $, \cdots \}$

(iii) $C= \{0,3, 6,9, 12, \cdots \}$

(vi) $D = \{10, 11,12, 13, 14,15\}$

(v) $E = \{0\}$

(vi) $\{1, 4, 9,16, \cdots 100\}$

(vii) $\{2, 4, 6, 8 , \cdots \}$

(viii) $\{5, 25, 125, 625, \cdots\}$

(i) $\{ x : x \in N , x < 7 \}$

(ii) $\{ x : x =$ $\frac{1}{n}$ $, n \in N \}$

(iii) $\{ x : x = 3n, n \in Z^+ \}$

(iv) $\{ x : x \in N, 9 < x < 16 \}$

(v) $\{ x : x = 0 \}$

(vi) $\{ x^2 : x \in N,1 \leq x \leq 10 \}$

(vii) $\{ x : x =2n, n \in N \}$

(viii) $\{ 5^n: n \in N, 1 \leq n \leq 4 \}$

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Question 3: List all the elements of the following sets:

(i) $A = \{x:x^2 \leq 10, x \in Z\}$

(ii) $B = \{ x:x =$ $\frac{1}{2n-1}$ $, 1 \leq x \leq 5\}$

(iii) $C = \{x:x \ is \ an \ integer, -$ $\frac{1}{2}$ $< x <$ $\frac{9}{2}$ $\}$

(vi) $D = \{x:x \ is \ a \ vowel \ in \ the \ word \ 'EQUATION' \}$

(v) $E =\{x: x \ is \ a \ month \ of \ a \ year \ not \ having \ 31 \ days\}$

(vi) $F = \{x: x \ is \ a \ letter \ of \ the \ word \ "MISSISIPPI" \}$

(i) $A = \{ 0, \pm 1, \pm 2, \pm 3 \}$

(ii) $B = \{ 1,$ $\frac{1}{3}$ $,$ $\frac{1}{5}$ $,$ $\frac{1}{7}$ $,$ $\frac{1}{9}$ $\}$

(iii) $C = \{ 0, 1, ,2 ,3, 4 \}$

(iv) $D = \{ A, E, I, O, U \}$

(v) $E = \{ February, April, June, September, November \}$

(vi) $F = \{ M, I, S, P \}$

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Question 4: Convert each of the sets on the left in the roster form with to the set-builder form:

(i) $\{A, P, L, E\}$

(ii) $\{5, -5\}$

(iii) $\{0\}$

(iv) $\{1, 2,5, 10 \}$

(v) $\{ A, H,J , R, S, T, N\}$

(vi) $\{2,5\}$

(i) $\{ x : x$ is a letter of a word $'APPLE' \}$

(ii) $\{ x : x^2 - 25 = 0 \}$

(iii) $\{ x : x + 5 = 5 , x \in Z \}$

(iv) $\{ x : x$ is a natural number and divisor of $10 \}$

(v) $\{ x : x$ is a letter of the word $'RAJASTHAN' \}$

(vi) $\{ x : x$ is a prime natural number and a divisor of 10 $\}$

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Question 5: Write the set of all vowels in the English alphabet which precede $q$.

$\{ a, e, i, o \}$

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Question 6: Write the set of all positive integers whose cube is odd.

$\{ x : x = 2n+1, n \in Z, n > 0 \}$

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Question 7: Write the set $\{$ $\frac{1}{2}$ $,$ $\frac{2}{5}$ $,$ $\frac{3}{10}$ $,$ $\frac{4}{17}$ $,$ $\frac{5}{26}$ $,$ $\frac{6}{37}$ $,$ $\frac{7}{50}$ $\}$

$\{ x : x =$ $\frac{n}{n^2+1}$ $, n \in N, n \leq 7 \}$

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