Set Builder Form

Q.

The set-builder representation of set $B=\{1,3,5,7,9\}$ is ______.

1. B = {x: x is a prime number less than 10}
2. B = {x: x is an odd natural number}
3. B = {x: x is an odd natural number less than 10}
4. B = {x: x is an odd number less than 10}

Q.

Match the following:

$$\begin{array}{cc}\text{Column A}& \text{Column B}\\ 1.A=\{x:xisanoddnaturalnumber\}& a.\{\frac{1}{2},\frac{1}{3},\frac{2}{3},\frac{3}{4},\frac{3}{5},\frac{5}{7}\}\\ 2.B=\{x:x=(n^2),n\in Nandx<100\}& b.\{1,4,9,16,25,........10000\}\\ 3.C=\{x:x=\frac{n}{n+2},n\in Nand1\le n\le 6\}& c.\{1,4,9,16,25,36,49,64,81\}\\ 4.D=\{x:xisaletterofthewordTRIGONOMETRY\}& d.\{G,E,I,M,N,O,R,T,Y\}\\ & e.\{1,3,5,7,9,...............\}\end{array}$$

1. 1 - e, 2 - b, 3 - a, 4 - d

2. 1 - e, 2 - c, 3 - a, 4 - d

3. 1 - c, 2 - b, 3 - d, 4 - e

4. 1 - c, 2 - b, 3 - a, 4 - d

Q. Let $P=\{\theta :\sin \theta -\cos \theta =\sqrt{2}\cos \theta \}$ and $Q=\{\theta :\sin \theta +\cos \theta =\sqrt{2}\sin \theta \}$ be two sets. Then

1. $P\subset QandQ-P\ne \varphi$
2. $Q\subset ̸P$
3. $P\subset ̸Q$
4. P = Q

Q.

The set-builder form of the set $\{\frac{1}{2},\frac{1}{4},\frac{1}{8},\frac{1}{16},\frac{1}{32},\frac{1}{64}\}$ is

1. $\{x:x=\frac{1}{2^m},\text{where}mϵW\text{and}m\le 6\}$

2. $\{x:x=\frac{1}{2^m},\text{where}mϵN\text{and}m\le 6\}$

3. $\{x:x=\frac{1}{2^m},\text{where}mϵN\text{and}m<6\}$

4. $\{x:x=\frac{1}{2^m},\text{where}mϵW\text{and}m<6\}$

Q.

The set $\{\frac{7}{8},\frac{8}{9},\frac{9}{10},\frac{10}{11},\frac{11}{12}\}$ expressed in set-builder form is ____. (Here, N represents the set of natural numbers.)

1. $\{x:x=\frac{n}{n+1},n\in N,7<n<11\}$

2. $\{x:x=\frac{n}{n+1},n\in N\}$

3. $\{x:x=\frac{n}{n+1},n\in N,7\le n\le 11\}$

4. $\{x:x=\frac{7n}{7n+1},n\in N\}$

Q.

The set builder form of "A is the set of whole numbers which are divisible by 5 and are less than 35" is _______________.

1. A = {$x:x=5n,n\in W,n<7$}

2. A = {$x:x=5n,n\in W$}

3. A = {$x:x=5n,n<7$}

4. A = {$x:x=5n,n\in W,n\le 7$}

Q.

The set - builder form of the set $\{\frac{4}{5},\frac{5}{6},\frac{6}{7},\frac{7}{8},\frac{8}{9},\frac{9}{10}\}$ is

1. $\{x:x=\frac{n}{n+1},\text{where}nϵN\text{and}4\le n\le 9\}$

2. $\{x:x=\frac{n}{n+1},\text{where}nϵN\text{and}4\le n<9\}$

3. $\{x:x=\frac{n}{n+1},\text{where}nϵN\text{and}4<n\le 9\}$

4. $\{x:x=\frac{n}{n+1},\text{where}nϵN\text{and}4<n<9\}$

Q. For the set {1, 3, 5, 7, 9}, the set builder form of representation is:
{x: x is an odd less than 10}

1. prime number
2. natural number
3. integer

Q. The set {$x:x$ is a letter in the word SELECT} in roster form is

1. $\left(S,E,L,C,T\right\}$
2. $\left(S,E,L\right\}$
3. $\left(S,E,L,C\right\}$

Q. Pair the following.

1. {x : x+5 = 0}
2. {y: y is an even prime}
3. {-5}
4. {p: p is an integer}
5. {.., -3, -2, -1, ..}
6. {2}