Set Builder Form

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 representation of the set B = {29, 31, 37, 41, 43, 47}, is ______ .

1. B = {x: x is an odd number more than 27 and less than 50}
2. B = {x: x is an odd number more than 25 and less than 50}
3. B = {x: x is a prime number more than 25 and less than 50}
4. B = {x: x is an odd number more than 50 and less than 25}

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. Find the complement of set A = {x : x is an integer, x < 3}.

1. {4, 5, 6...}
2. {3, 4, 5...}
3. {-4, -5, ...}
4. {-5, -6, ...}

Q.

State, whether the following pairs of sets are equal or not:

(i) A=$\{2,4,6,8\}$ and $B=\{2n:n\in Nandn<5\}$

(ii) $M=\{x:x\in Wandx+3<8\}andN=\{y:y=2n-1,n\in Nandn<5\}$

(iii) $E=\{x:x^2+8x-9=0\}andF=\{1,-9\}$

(iv) $A=\{x:x\in ,x<3\}andB=\{y:y^2-3y+2=0\}$ Two sets are equal, if both the sets have same (identical) elements.

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

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

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

Q.

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.

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 of even prime numbers that are greater than 2 is a/an _____________.

1. disjoint set

2. empty set

3. singleton set

4. infinite set

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. 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.

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.

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. Which of the following collections are sets?
(i) The collection of prime numbers.
(ii) The collection of easy sub topics in this chapter.
(iii) The collection of good teachers in your school.
(iv) The collection of girls in your class.
(v) The collection of odd natural numbers.

1. $\left(i\right),\left(ii\right),\left(iv\right)$ only
2. $\left(ii\right),\left(iii\right),\left(v\right)$ only
3. $\left(iii\right),\left(iv\right)$ only
4. $\left(i\right),\left(iv\right),\left(v\right)$ only

Q.

1. True

2. False

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}

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. Find the complement of set A = {x : x is an integer, x < 3}.

1. {4, 5, 6...}
2. {-5, -6, ...}
3. {-4, -5, ...}
4. {3, 4, 5...}

Q. Find the complement of set A = {x : x is an integer, x < 3}.

1. {4, 5, 6...}
2. {-4, -5, ...}
3. {3, 4, 5...}
4. {-5, -6, ...}

Q. If $\theta +\varphi =\alpha$ and $\tan \theta =k\tan \varphi$, then prove that $\sin \left(\theta -\varphi \right)=\frac{k-1}{k+1}\sin \alpha$.

Q.

The set of even prime numbers that are greater than 2 is a/an _____________.

1. disjoint set

2. infinite set

3. empty set

4. singleton set

Q. Find the complement of set A = {x : x is an integer, x < 3}.

1. {3, 4, 5...}
2. {-4, -5, ...}
3. {-5, -6, ...}
4. {4, 5, 6...}

Q. A can do a piece of work in $10$ days , B in $18$ days and A, B and C together in $4$ days. In how many days will C alone can do it?

1. $6\frac{2}{3}$
2. $15\frac{17}{19}$
3. $10\frac{10}{17}$
4. $11\frac{9}{4}$

Q. Three consecutive whole numbers are such that if they be divided by $5,3$ and $4$ respectively; the sum of their quotients is $40$. Find the numbers.

1. $20,35$ and $22$
2. $40,11$ and $25$
3. $5,5$ and $8$
4. $50,51$ and $52$

Q. The set builder representation of the set B = {29, 31, 37, 41, 43, 47}, is ______ .

1. B = {x: x is an odd number more than 27 and less than 50}
2. B = {x: x is an odd number more than 50 and less than 25}
3. B = {x: x is a prime number more than 25 and less than 50}
4. B = {x: x is an odd number more than 25 and less than 50}

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

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

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

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

Q. Find the complement of set A = {x : x is an integer, x < 3}.

1. {-4, -5, ...}
2. {4, 5, 6...}
3. {-5, -6, ...}
4. {3, 4, 5...}