Question 4:
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}
Answers
Answer:
(i) {3, 6, 9, 12} = {x: x = 3n, n∈ N and 1 ≤ n ≤ 4}
(ii) {2, 4, 8, 16, 32}
It can be seen that 2 = 21, 4 = 22, 8 = 23, 16 = 24, and 32 = 25.
∴ {2, 4, 8, 16, 32} = {x: x = 2n, n∈ N and 1 ≤ n ≤ 5}
(iii) {5, 25, 125, 625}
It can be seen that 5 = 51, 25 = 52, 125 = 53, and 625 = 54.
∴ {5, 25, 125, 625} = {x: x = 5n, n∈N and 1 ≤ n ≤ 4}
(iv) {2, 4, 6 …}
It is a set of all even natural numbers.
∴ {2, 4, 6 …} = {x: x is an even natural number}
(v) {1, 4, 9 … 100}
It can be seen that 1 = 12, 4 = 22, 9 = 32 …100 = 102.
∴ {1, 4, 9… 100} = {x: x = n2, n∈N and 1 ≤ n ≤ 10}
want to learn sets;
<1> Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈or ∉ in the blank spaces:
(i) 5…A (ii) 8…A (iii) 0…A
(iv) 4…A (v) 2…A (vi) 10…A
see this:
brainly.in/question/26536068
<2> Which of the following are sets? Justify our answer.
(i) The collection of all months of a year beginning with the letter J.
(ii) The collection of ten most talented writers of India.
(iii) A team of eleven best-cricket batsmen of the world.
(iv) The collection of all boys in your class.
(v) The collection of all natural numbers less than 100.
(vi) A collection of novels written by the writer Munshi Prem Chand.
(vii) The collection of all even integers.
(viii) The collection of questions in this Chapter.
(ix) A collection of most dangerous animals of the world.
see this;
brainly.in/question/26535915
Answer:
1) { X|X is a multiple of 3 and 2<X<13}
2) {X|X =2^n ,n∈N,and 1<n<5
3) { X|X = 5^n , n∈N and 1 ≤ n ≤ 4}
4) {x|x is a multiple of 2 and 2≤x ≤...
5) {x|x is a set of natural no. and 1 ≤x ≤100