# Set Builder Form

## Trending Questions

**Q.**

Describe the following sets in set-builder form :

(i) A = {1, 2, 3, 4, 5, 6}

(ii) B = {1, 12, 13, 14, 14, ......}

(iii) C = {0, 3, 6, 9, 12, .....}

(iv) D = {10, 11, 12, 13, 14, 15}

(v) E = {0} (vi) {1, 4, 9, 16, ...., 100}

(vii) {2, 4, 6, 8, ....}

(viii) {5, 25, 125, 625}

**Q.**The set builder form of {2, 4, 6, 8, 10} is

- {x:x=2n where n∈N such that n<6}
- {x:x=2n+1 where n∈{1, 2, 3}}
- {x:x=2n where n∈Z such that n<6}
- {x:x is even natural number less than 10}

**Q.**

In set -builde method the null set is represented by

{ }

{x : x= x}

ϕ

{x:x≠x}

**Q.**The set builder form of {12, 23, 34, 45, 56} is

- {x:x=nn+1, where n is a natural number and 1≤n≤6}
- {x:x=nn+1, where n is a natural number and 1≤n≤5}
- {x:x=nn+1, where n is a natural number and 2≤n≤6}
- {x:x=nn−1, where n is a natural number and 1≤n≤5}

**Q.**

Write the following sets in the set-builder form:

(i) (3, 6, 9, 12) (ii) {2, 4, 8, 16, 32}

(iii) {5, 25, 125, 625} (iv) {2, 4, 6 …}

(v) {1, 4, 9 … 100}

**Q.**

Write the set {12, 25, 310, 417, 526, 637, 750} in the set -builder form.

**Q.**Let A be a set of all real numbers except 1 and 0 be an operation on A defined by aob = a+b-ab for all a, b€A. Prove that A is closed under a given operation.

**Q.**Which of the following pairs of sets are equal? Justify your answer.

(i) X, the set of letters in ALLOY and B, the set of letters in LOYAL

(ii) A={n:n∈Z and n2≤4} and B={x:x∈R and x2−3x+2=0}

**Q.**The figure shows a relation between the sets P and Q. Write this relation

(i) In set builder form

(ii) In roster form

What is its domain and range?

**Q.**The most appropriate option for the following sets

A is set of letters of the word 'debit card'

B is the set of letters of the word 'bad credit'

- A and B are equivalent sets
- A and B are unequal sets
- A and B are similar sets
- A and B are identical sets

**Q.**Write the set {12, 23, 34, 45, 56, 67} in the set-builder form.

**Q.**To represent a set, how many notations exist

- only one
- More than 2
- 2
- 0

**Q.**From the sets given below, select equal sets:

A={2, 4, 8, 12}, B={1, 2, 3, 4}, C={4, 8, 12, 14}, D={3, 1, 4, 2}

E={−1, 1}, F={0, a}, G={1, −1}, H={0, 1}

**Q.**

Match each of the sets on the left in the roster form with the same set on the right described in the set -builder form :

(i) {A, P, L, E} (i) { x:x+5=5, x ϵ Z}

(ii) {5, -5} (ii) {x : x is a prime natural number and a divisor of 10}

(iii) {0} (iii) {x : x is a letter of the word "RAJASTHAN"}

(iv) {1, 2, 5, 10} (iv) {x : x is a natural number and divisor of 10}

(v) {A, H, J, R, S T, N} (v) {x:x2−25=0}

(vi) {2, 5} (vi) {x : X is a letter of the word "APPLE"}

**Q.**Express each of the following sets in set-builder notation (form):

(ii) {2, 3, 5, 7, 11, 13, …}

**Q.**

What is ${}^{n}{P}_{r}$the formula?

**Q.**

Find the minimum value of 5cosA + 12sinA + 12

**Q.**The set {6, 36, 216, 1296} can be written in Set builder form as:

- {x:x=6n, n∈N, n≤5}
- {x:x=6n, n∈N, n≤4}
- {x:x=6n, n∈W, n≤4}
- {x:x=6n, n∈W, n≤5}

**Q.**

Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universals set (s) for all the three sets A, B and C

(i) {0, 1, 2, 3, 4, 5, 6}

(ii) Φ

(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

(iv) {1, 2, 3, 4, 5, 6, 7, 8}

**Q.**Describe the following set in the set-builder form:

(viii) {5, 25, 125, 625}

**Q.**Write the following sets in set-builder (Rule Method) form:

B1=6, 9, 12, 15, .........

**Q.**The set builder form of {2, 4, 6, 8, 10} is

- {x:x is even natural number less than 10}
- {x:x=2n where n∈N such that n<6}
- {x:x=2n+1 where n∈{1, 2, 3}}
- {x:x=2n where n∈Z such that n<6}

**Q.**Write the following sets in roster (Tabular) form:

A6={x:x=nn+2;n

∈Nandn>5}

rm:**Q.**The general value of θ satisfying equation tan3θ−tan2θ−tanθ=0

- nπ
- nπ4
- nπ2
- nπ3

**Q.**Express the given sets in roster form:

(x) F = Set of factors of 24

**Q.**The set builder form of {12, 23, 34, 45, 56} is

- {x:x=nn+1, where n is a natural number and 1≤n≤6}
- {x:x=nn+1, where n is a natural number and 1≤n≤5}
- {x:x=nn+1, where n is a natural number and 2≤n≤6}
- {x:x=nn−1, where n is a natural number and 1≤n≤5}

**Q.**If $A=\left[\begin{array}{cc}2& -1\\ 3& -2\end{array}\right],\mathrm{then}{A}^{n}=$

(a) $A=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$, if n is an even natural number

(b) $A=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$, if n is an odd natural number

(c) $A=\left[\begin{array}{cc}-1& 0\\ 0& 1\end{array}\right],\mathrm{if}n\in N$

(d) none of these

**Q.**The general solution of the equation tanθ+tan4θ+tan7θ=tanθtan4θtan7θ is

**Q.**

Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by

{(*a*,
*b*):
*a*,
*b*
∈
A, *b*
is exactly divisible by *a*}.

(i) Write R in roster form

(ii) Find the domain of R

(iii) Find the range of R.

**Q.**A set Y containing all elements x such that x is a whole number less than 10 can be represented in Set-builder form as:

- Y={x:x<11 & x∈W}
- Y={x:x<10 & x∈W}
- Y={x:x>10 & x∈W}