Set Builder Method

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. $\{x:x=\frac{1}{2^n},\text{where}n\in N\text{and}n\le 6\}$

2. $\{x:x=\frac{1}{2^n},\text{where}n\in N\text{and}n<6\}$

3. $\{x:x=\frac{1}{2^n},\text{where}n\in W\text{and}n<6\}$

4. $\{x:x=\frac{1}{2^n},\text{where}n\in W\text{and}n\le 6\}$

Q.

If $f\left(x\right)=\frac{x}{x-1},x\ne 1$, then ${\left(fofo...of\right)}_{\left(19times\right)}\left(x\right)$ is equal to

1. $\frac{x}{\left(x-1\right)}$

2. ${\left[\frac{x}{x-1}\right]}^{19}$

3. $\frac{19x}{x-1}$

4. $x$

Q.

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

1. $\{x:x=\frac{1}{2^n},\text{where}n\in W\text{and}4<n\le 6\}$

2. $\{x:x=\frac{1}{2^n},\text{where}n\in N\text{and}4\le n\le 6\}$

3. $\{x:x=\frac{1}{2^n},\text{where}n\in N\text{and}4\le n<6\}$

4. $\{x:x=\frac{1}{2^n},\text{where}n\in W\text{and}4<n<6\}$

Q.

The set - builder form of the set $\{\frac{2}{3},\frac{3}{4},\frac{4}{5},\frac{5}{6},\frac{6}{7}\}$ is

1. $\{x:x=\frac{n}{n+1},\text{where}nϵN\text{and}2<n\le 6\}$

2. $\{x:x=\frac{n}{n+1},\text{where}nϵN\text{and}2\le n\le 6\}$

3. $\{x:x=\frac{n}{n+1},\text{where}nϵN\text{and}2<n<6\}$

4. $\{x:x=\frac{n}{n+1},\text{where}nϵN\text{and}2\le n<6\}$

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

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

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 {$\frac{7}{8},\frac{8}{9},\frac{9}{10},\frac{10}{11},\frac{11}{12}$} expressed in set builder form is

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

2. {$x:x=\frac{n}{n+1},n\in N7\le n\le 11$}

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

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

Q.

If B = {1, 3, 5, 7, 9}, then set-builder representation of B 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. 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. If S = {y : y = x^3, x is a negative integer}, then _____ belongs to S.

1. -4
2. 8
3. 27
4. -1

Q. What will be the set - builder form of he set A = {5, 10, 15, 20, 25, 30} ?

Q.

Statewhether the following statements are True or False:

(a) Thesum of three odd numbers is even.

(b) Thesum of two odd numbers and one even number is even.

(c) Theproduct of three odd numbers is odd.

(d) If aneven number is divided by 2, the quotient is always odd.

(e) Allprime numbers are odd.

(f) Primenumbers do not have any factors.

(g) Sum oftwo prime numbers is always even.

(h) 2 isthe only even prime number.

(i) Alleven numbers are composite numbers.

(j) Theproduct of two even numbers is always even.

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