\displaystyle \textbf{Question 1: }\text{Describe the following sets in roster form:}
\displaystyle \text{(i) }\{x:x\text{ is a letter before }e\text{ 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 and }10<x<20\}
\displaystyle \text{(iv) }\{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\}
\displaystyle \text{(viii) The set of all letters in the word 'Trigonometry'.}
\displaystyle \text{(ix) The set of all letters in the word 'Better'.}
\displaystyle \textbf{Answer:}
\displaystyle \text{(i) }\{a,b,c,d\}
\displaystyle \text{(ii) }\{1,2,3,4\}
\displaystyle \text{(iii) }\{11,13,17,19\}
\displaystyle \text{(iv) }\{2,4,6,8,10,\ldots\}
\displaystyle \text{(v) }\varnothing
\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,t,y\}
\displaystyle \text{(ix) }\{B,e,t,r\}
\displaystyle \\

\displaystyle \textbf{Question 2: }\text{Describe the following sets in set-builder form:}
\displaystyle \text{(i) }A=\{1,2,3,4,5,6\}
\displaystyle \text{(ii) }B=\left\{1,\frac12,\frac13,\frac14,\frac15,\cdots\right\}
\displaystyle \text{(iii) }C=\{0,3,6,9,12,\cdots\}
\displaystyle \text{(iv) }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 \textbf{Answer:}
\displaystyle \text{(i) }\{x:x\in N,\ x<7\}
\displaystyle \text{(ii) }\left\{x:x=\frac1n,\ n\in N\right\}
\displaystyle \text{(iii) }\{x:x=3n,\ n\in W\}
\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\le x\le10\}
\displaystyle \text{(vii) }\{x:x=2n,\ n\in N\}
\displaystyle \text{(viii) }\{5^n:n\in N,\ n\ge1\}
\displaystyle \\

\displaystyle \textbf{Question 3: }\text{List all the elements of the following sets:}
\displaystyle \text{(i) }A=\{x:x^2\le10,\ x\in Z\}
\displaystyle \text{(ii) }B=\left\{x:x=\frac{1}{2n-1},\ 1\le n\le5\right\}
\displaystyle \text{(iii) }C=\left\{x:x\text{ is an integer, }-\frac12<x<\frac92\right\}
\displaystyle \text{(iv) }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\text{ days}\}
\displaystyle \text{(vi) }F=\{x:x\text{ is a letter of the word "MISSISIPPI"}\}
\displaystyle \textbf{Answer:}
\displaystyle \text{(i) }A=\{0,\pm1,\pm2,\pm3\}
\displaystyle \text{(ii) }B=\left\{1,\frac13,\frac15,\frac17,\frac19\right\}
\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 \\

\displaystyle \textbf{Question 4: }\text{Convert each of the following sets from roster form to 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 \textbf{Answer:}
\displaystyle \text{(i) }\{x:x\text{ is a letter of the 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 a 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 \\

\displaystyle \textbf{Question 5: }\text{Write the set of all vowels in the English alphabet which precede }q.
\displaystyle \textbf{Answer:}
\displaystyle \{a,e,i,o\}
\displaystyle \\

\displaystyle \textbf{Question 6: }\text{Write the set of all positive integers whose cube is odd.}
\displaystyle \textbf{Answer:}
\displaystyle \{x:x=2n+1,\ n\in W\}
\displaystyle \\

\displaystyle \textbf{Question 7: }\text{Write the set }\left\{\frac12,\frac25,\frac3{10},\frac4{17},\frac5{26},\frac6{37},\frac7{50}\right\}
\displaystyle \text{in set-builder form.}
\displaystyle \textbf{Answer:}
\displaystyle \left\{x:x=\frac{n}{n^2+1},\ n\in N,\ n\le7\right\}
\displaystyle \\

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