Question 1: Describe the following sets in Roster form:

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

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

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

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

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

$\displaystyle \text{(vi) } \{x : x \text{ is a prime number which is a divisor of } 60 \}$

$\displaystyle \text{(vii) } \{x:x \text{ is a two digit number such that the sum of its digits is } 8\}$

(viii) The set of all letters in the word  $\displaystyle \text{ 'Trigonometry'}$

(ix) The set of all letters in the word ‘Better’

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

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

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

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

$\displaystyle \text{(v) } \phi$

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

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

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

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

$\displaystyle \\$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$\displaystyle \\$

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

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

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

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

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

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

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

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

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

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

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

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

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

$\displaystyle \\$

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

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

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

$\displaystyle \text{(iii) } \{0\}$

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

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

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

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

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

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

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

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

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

$\displaystyle \\$

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

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

$\displaystyle \\$

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

$\displaystyle \{ x : x = 2n+1, n \in Z, n > 0 \}$
$\displaystyle \\$
$\displaystyle \text{Question 7: Write the set } \{ \frac{1}{2} , \frac{2}{5} , \frac{3}{10} , \frac{4}{17} , \frac{5}{26} , \frac{6}{37} , \frac{7}{50} \}$
$\displaystyle \displaystyle \{ x : x = \frac{n}{n^2+1} , n \in N, n \leq 7 \}$