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’

Answer:

(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\}

Answer:

(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" \}

Answer:

(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\}

Answer:

(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 .

Answer:

\{ a, e, i, o \}

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

Answer:

\{ 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} \}

Answer:

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

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