Set Builder Form
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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}
- {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}
In set -builde method the null set is represented by
{ }
{x : x= x}
ϕ
{x:x≠x}
- {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}
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}
Write the set {12, 25, 310, 417, 526, 637, 750} in the set -builder form.
(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}
(i) In set builder form
(ii) In roster form
What is its domain and range?
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
- only one
- More than 2
- 2
- 0
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}
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"}
(ii) {2, 3, 5, 7, 11, 13, …}
What is the formula?
Find the minimum value of 5cosA + 12sinA + 12
- {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}
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}
(viii) {5, 25, 125, 625}
B1=6, 9, 12, 15, .........
- {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}
A6={x:x=nn+2;n
∈Nandn>5}
rm:- nπ
- nπ4
- nπ2
- nπ3
(x) F = Set of factors of 24
- {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}
(a) , if n is an even natural number
(b) , if n is an odd natural number
(c)
(d) none of these
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.
- Y={x:x<11 & x∈W}
- Y={x:x<10 & x∈W}
- Y={x:x>10 & x∈W}